Research Achievements

The team has made significant progress in general relativity and geometric analysis. Researcher Xuefeng Feng, in collaboration with others (including Professor Shing-Tung Yau), proved that axisymmetric black holes with angular momentum satisfy a generalized first law, which leads to a Penrose-type geometric inequality for such black holes, thereby deepening the understanding of fundamental black hole properties (Class. Quantum Grav. 2025). In random geometry, the team pioneered the application of Weil–Petersson random surface theory to the study of Steklov eigenvalues, revealing typical behavior in the spectral properties of manifolds (Math. Z. 2024). At the same time, the team achieved key breakthroughs in geometric flows and their applications: Professor Yi Li, together with collaborators, partially resolved the open problem of long-time existence for solutions to the Laplacian flow and established monotonicity results for parabolic frequency functionals as well as gradient estimates for the heat equation under this flow (J. Funct. Anal. 2026; Calc. Var. Partial Differ. Equ. 2025), providing new tools for research in geometric analysis and partial differential equations.

Research Outputs

• Xuefeng Feng; Ruodi Yan; Sijie Gao; Yun-Kau Lau; Shing-Tung Yau.Geometric inequality for axisymmetric black holes with angular momentum; Class. Quantum Grav. 42 065022;2025
  This paper is to understand the Penrose inequality for black holes with angular momentum, an axisymmetric, vacuum, asymptotically Euclidean initial data set subject to certain quasi-stationary conditions is considered for a case study. In terms of spinors, a generalised first law for rotating black holes (possibly with multi-connected horizon located along the symmetry axis) is then proven and may be regarded as a Penrose-type inequality for black holes with angular momentum.
• Chuanhuan Li; Yi Li. Curvature pinching estimate under the Laplacian G2 flow, J. Funct. Anal., 290(2026), no. 1, Paper No. 111199, 29 pp. MR4964139.
  This paper presents a pinching estimate for the Ricci curvature, based on which the long-time existence of solutions to the Laplace flow is established, thereby partially addressing an open question.
• Xiaolong Han; Yuxin He; Han Hong. Large Steklov eigenvalues on hyperbolic surfaces. Math. Z. 308 (2024), Paper No. 37, 21 pages.
  We first construct a sequence of hyperbolic surfaces with connected geodesic boundary such that the first normalized Steklov eigenvalue  tends to infinity. We then prove some results of the type that the Weil-Petersson probability that a hyperbolic surface of genus g and n boundary components have Steklov eigenvalues tending to infinity tends to 1 as g tends to infinity. We are among the first to introduced using Weil-Petersson random hyperbolic surfaces in studying Steklov eigenvalues.
• Chuanhuan Li;Yi Li; Kairui Xu. Gradient estimates and parabolic frequency under the Laplacian G2 flow, Calc. Var. Partial Differential Equations, 64(2025), no. 4, Paper No. 121, 28 pp. MR4882932.
  This paper provides the first rigorous construction of gradient estimates under the Laplace flow and, as a direct consequence, establishes the monotonicity of several frequency functionals as well as a backward uniqueness result.
• S.-C. Chang; Y. Han; C. Lin; C.-T. Wu. Convergence of the Sasaki-Ricci Flow on Sasakian 5-Manifolds of General Type, International Journal of Mathematics, (2026) pp 1-47.
  In this paper, we show that the uniform L⁴-bound of the transverse Ricci curvature along the Sasaki-Ricci flow on a compact quasi-regular Sasakian (2n+1)-manifold M of general type. As an application, any solution of the normalized Sasaki-Ricci flow converges in the Cheeger-Gromov sense to the unique singular Sasaki η-Einstein metric on the transverse canonical model of M for n≤3. In particular, for n=2, the canonical model is a S¹-orbibundle over the unique Kähler-Einstein orbifold surface with finite point orbifold singularities. The floating foliation (-2)-curves in M will be contracted to orbifold points by the Sasaki-Ricci flow as t→∞.
• Yi Li; Qianwei Zhang. Gradient estimates on graphs with the CD(n,-K) condition, J. Geom. Anal., 35(2025), no. 10, Paper No. 324, 25 pp. MR4948694.
  This paper investigates gradient estimates on graphs satisfying some curvature condition. Our study focuses on gradient estimates for positive solutions of the heat equation. Additionally, the estimate is extended to a heat-type equation . Furthermore, we utilize these estimates to derive heat kernel bounds and Harnack inequalities.
• Ning Cao; Feida Jiang. Entire solutions and asymptotic behavior to a class of parabolic k-Hessian equations. Discrete Contin. Dyn. Syst. 48 (2026), 196–230.
  A systematic study the radial ancient solutions in the separate variable form to a kind of parabolic k-Hessian equations with parameter α is made. This paper discusses the entire existence, non-existence, uniqueness and fine asymptotic behavior under different α.
• Yiyu Lin; Dongyu Fang; Jiechen Jin; Chenye Li. The holographic entanglement pattern of BTZ planar black hole from a thread perspective, JHEP 10 (2025) 072.
  In this paper, we study the holographic quantum entanglement structure in the finite-temperature CFT state/planar BTZ black hole correspondence from the perspective of entanglement threads. Unlike previous studies based on bit threads, these entanglement threads provide a more detailed characterization of the contribution sources to the von Neumann entropy of boundary subregions, in particular by quantitatively deriving the flux function of entanglement threads that traverse the wormhole horizon and connect the two asymptotic boundaries. Since entanglement threads are naturally and closely related to tensor network states, the results are argued to imply the existence of the perfect-type entanglement formed jointly by the entanglement threads crossing the wormhole and the internal threads in the single-sided boundary. We also discuss the close connections of this work with concepts such as bit threads and partial entanglement entropy.
• Zhiqiang Miao; Xuefeng Feng; Zhen Pan; Huan Yang. Relativistic excitation of compact stars; Phys. Rev. D 112, 104054;2025
  This paper study the excitation of a compact star under the influence of external gravitational driving in the relativistic regime. Using a model setup in which a wave with constant frequency is injected from past null infinity and scattered by the star to future null infinity, we show that the scattering coefficient encodes rich information of the star. 
• Shuanglin Huang; Xuefeng Feng; Yun-Kau, Lau.Angular velocity of rotating black holes—a new way to construct initial data for binary black holes;Class. Quantum Grav. 42 235021;2025
  This paper construct initial data sets for binary rotating black holes by prescribing the angular velocities of the two black holes at their horizons. When the angular velocities are non-uniform and deviate from a constant value at the horizons, new gravitational waveforms are generated which display certain oscillatory pattern reminiscent of that of quasi-normal ringing in the inspiral phase before merger takes place.
• H. Adami; M. M. Sheikh-Jabbari; V. Taghiloo. Gravitational stress tensor and current at null infinity in three dimensions, Physics Letters B 855 (2024) 138835
  This work establishes the intrinsic conserved gravitational stress tensor and current associated with null infinity in three-dimensional asymptotically flat spacetimes. These objects are identified as the canonical conjugates of the degenerate metric and Ehresmann connection of boundary Carrollian geometry. By introducing a torsional affine connection at null infinity, the conservation laws are shown to reproduce the Bondi mass and angular momentum balance equations. The results provide a concrete realization of flat-space holography in three dimensions and naturally lead to an asymptotically flat fluid/gravity correspondence. Requiring a well-defined action principle further yields a Schwarzian action governing reparametrization dynamics on the celestial circle, consistent with codimension-two holography in 3d flat spacetimes.
• H. Adami; M. Golshani; M. M. Sheikh-Jabbari; V. Taghiloo, M. H. Vahidinia.
  Covariant phase space formalism for fluctuating boundaries, Journal of High Energy Physics 09 (2024) 157.
  This paper extends the covariant phase space formalism for gauge and gravity theories to spacetimes with fluctuating boundaries. A systematic analysis of the symplectic structure, its ambiguities, and conservation properties is presented in arbitrary dimensions. It is shown that allowing boundary fluctuations renders all surface charges integrable, resolving a long-standing obstruction in charge construction. The work further analyzes charge algebras, central extensions, fluxes, and conservation laws, and discusses implications for memory effects and semiclassical aspects of black holes. The framework provides a unified and robust foundation for boundary dynamics in gravitational theories.
• Jiangwen Wang;Yunwen Yin;Feida Jiang, Regularity of Solutions to Degenerate Normalized p-Laplacian Equation with General Variable Exponents. Potential Anal. 63, 1963–2000 (2025).
  This paper establishes local C1,α regularity of viscosity solutions to normalized p-Laplace equations with two phase gradient degeneracy of general variable exponents. This paper also prove almost optimal pointwise C1,α regularity for degenerate free transmission problem related to normalized p-Laplacian.
• Wendi Xu, Ground state solutions to some indefinite nonlinear Schr\”{o}dinger equations on lattice graphs, Acta Math. Sin. (Engl. Ser.) 41 (2025), no. 5, 1279–1295.
  This paper consider the Schrödinger type equation −Δu+V(x)u=f(x,u) on the lattice graph with indefinite variational functional and obtain ground state solutions by using the method of generalized Nehari manifold.
• Jiangwen Wang;Feida Jiang, Regularity of solutions for degenerate or singular fully nonlinear integro-differential equations. Commun. Contemp. Math. (2025) 2550080 (36 pages)
  A series of regularity results for solutions to a degenerate or singular fully nonlinear integro-differential equation are proved in this paper.
• Chuanhuan Li;Yi Li; Kairui Xu; Jichun Zhu. Parabolic frequency monotonicity for two nonlinear equations under Ricci flow. Acta Math. Sci. Ser. B (Engl. Ed.) 46 (2026), no. 2, 752–766. MR5005679.
  In this paper, we study the parabolic frequency for positive solutions of two nonlinear parabolic equations under the Ricci flow on closed manifolds. We establish the monotonicity of the parabolic frequency for the solutions of two nonlinear parabolic equations with bounded Ricci curvature. Subsequently, we apply the parabolic frequency monotonicity to derive some integral type Harnack inequalities.
• Huyuan Chen, On m-order logarithmic Laplacians and the applications, Analysis and Applications,24(2), 419-461(2026)
  This paper investigates the existence of solutions to the mean field equation on a connected finite graph using the method of variations.
• Minyang Cao;Feida Jiang; Wenhao Zhu. Purely interior Hessian estimates for a kind of Monge-Ampere equations. Nonlinear Differ. Equ. Appl. 33 (2026) article number 19.
  This paper derives purely Hessian estimates for a kind of two dimensional Monge-Ampere equation via Jacobi inequality and the method of constructing double logarithmic auxiliary function.
• Huyuan Chen; Long Chen. Counting function and lower bounds for Dirichlet eigenvalues of the m-order logarithmic Laplacian, Complex Variables and elliptic equations.
  This paper discusses the properties of Dirichlet eigenvalues for the higher-order logarithmic Laplacian operator with zero boundary conditions on bounded domains. Initially, this paper studied the properties of the counting function of eigenvalues, particularly its limit, to further obtain upper and lower bounds estimates for the eigenvalues.
• Yi Li; Qianwei Zhang. Variational approach to the mean field equation on finite graphs, J. Math. Anal. Appl., 551(2025), no. 1, Paper No. 129614, 21 pp. MR4901552.
  This paper derives the expression of the high-order logarithmic Laplacian operator by expanding the order of the fractional Laplacian operator, and provides the Taylor expansion of the Riesz potential operator from the logarithmic Laplacian operator. It discusses the basic properties of this type of operator, as well as the existence of Dirichlet eigenvalues and related eigenfunctions with zero boundary conditions on bounded domains.

The team has produced systematic achievements at the cutting edge of the intersection between mathematics and physics. Professor Yehao Zhou and his collaborators have advanced the connection between quantum field theory and algebra across multiple dimensions. This includes the construction of deformed double current algebras and matrix extended W∞-algebras from the theory of M2-M5 brane intersections (Commun. Math. Phys. 2025), providing a new paradigm for understanding the physical correlations between M-theory and algebraic structures. Simultaneously, the team has made significant progress in the field of algebraic geometry. Professor Arkadij Bojko and his collaborator conducted the first study of equivariant Segre and Verlinde invariants of Quot schemes on complex spaces, pushing forward frontier research into related invariants in enumerative geometry (Moduli 2025). Professor Long Wang and his collaborator investigated the arithmetic dynamics of cohomologically hyperbolic maps, providing new evidence for the Zariski dense orbit conjecture and proving that arithmetic degrees can be transcendental numbers (Trans. Amer. Math. Soc. 2024), thereby advancing research in the field of arithmetic dynamics.

Research Outputs

1. Ioana Coman, Myungbo Shim, Masahito Yamazaki and Yehao Zhou, Affine W-Algebras and Miura Maps from 3d N=4 Non-Abelian Quiver Gauge Theories, Communications in Mathematical Physics (2025) 406:122. 2.
   This paper constructs a chiral quantization framework for Nakajima quiver varieties and applies it to the study of vertex operator algebras on the two-dimensional boundary of three-dimensional N=4 non-Abelian quiver gauge theories. Using a novel localization technique proposed in this work, we reveal that affine W-algebras and their Miura maps arise as global sections of these chiral quantizations.
2. Sen Hu, Si Li, Dongheng Ye and Yehao Zhou, Quantum Algebra of Chern-Simons Matrix Model and Large N Limit, Annales Henri Poincaré (2025).
   This paper discovers a novel deformed double current algebra structure of the local observables in the Chern-Simons matrix model. This points to a conjectural completed description of the large N limit of the local observable algebra of this matrix model, and sheds lights on the study of the fractional quantum Hall states.
3. Davide Gaiotto, Miroslav Rapcak, Yehao Zhou, Deformed Double Current Algebras, Matrix Extended W∞-Algebras, Coproducts, and Intertwiners from the M2-M5 Intersection, Communications in Mathematical Physics (2025) 406:311.
   This paper generalizes the renowned relationship between deformed double current algebras, W∞-Algebras, and affine Yangian of gl(1) to arbitrary rank. A new presentation of affine Yangian of gl(K) is dicovered.
4. Arkadij Bojko, Jiahui Huang, Equivariant Segre and Verlinde invariants for Quot schemes. Moduli. 2025;2:e14.
   Segre and Verlinde series have been studied by Pandharipande et al., including virtual geometries of Quot schemes on surfaces and Calabi-Yau 4-folds. Our work is the first to address the equivariant setting for both C^2 and C^4 by examining higher degree contributions which have no compact analogue.
5. Cécile Gachet, Hsueh-Yung Lin, Long Wang, Nef cones of fiber products and an application to the cone conjecture, Forum of Mathematics, Sigma, Volume 12, 2024, e28.
   This article studies the decomposition of the nef cone of a fiber product over a curve, and applies it to the Kawammata-Morrison-Totaro cone conjecture for Schoen varieties.
6. Yohsuke Matsuzawa, Long Wang, Arithmetic degrees and Zariski dense orbits of cohomologically hyperbolic maps. Transactions of the American Mathematical Society, Volume 377, 2024, Issue 9, pp. 6311–6340.
   This paper investigates cohomological hyperbolic rational mappings, including the lower bound of the arithmetic degree, the existence of Zariski dense orbits, and the finiteness of preperiodic points. In particular, the authors prove that the arithmetic degree can be a transcendental number.

The team has made some breakthroughs in the fields of arithmetic geometry and the Langlands program. Associate Professor Dingxin Zhang and his collaborators revealed a hidden cancellation structure among Frobenius eigenvalupes in the rigid cohomology of  varieties over finite fields (Compos. Math. 2025), and constructed a connection between the deformation space of Calabi–Yau singularities and automorphic forms, thereby proving the automorphy and finiteness of some generators of the Yamaguchi–Yau algebra, providing an affirmative answer to a question posed by Shing-Tung Yau (Commun. Number Theory Phys. 2025). Professor Chung-Pang Mok proved a Gross–Zagier formula for Stark–Heegner points over the genus field of real quadratic fields, advancing research on classical problems in number theory (Pure Appl. Math. Q. 2025).

Research Outputs

1. Daqing Wan, Dingxin Zhang, Revisiting Dwork cohomology: visibility and divisibility of Frobenius eigenvalues in rigid cohomology, Compositio Mathematica 161 (2025), 1215–1249.
   This paper uncovers a hidden structure governing the internal cancellation of Frobenius eigenvalues in the zeta functions of varieties in algebraic tori over a finite field for rigid cohomology. This phenomenon points to novel, conjectural behavior of Frobenius eigenvalues in the ℓ-adic setting.
2. Chung Pang Mok, On a complex analytic Gross-Zagier formula for Stark-Heegner points over genus fields of real quadratic fields and applications, Pure and Applied Mathematics Quarterly, Volume 21 (2025), Number 5, 1939-1958.
   The theory of Stark-Heegner points is the central part of the program initiated by the Canadian Mathematician Henri Darmon, with the goal of solving Hilbert’s 12^th problem using p-adic analytic methods. In this paper, we use the generalized Gross-Zagier formula for classical Heegner points, as established by Shouwu Zhang, combined with the p-adic uniformization theory of Shimura curves, to show that the Stark-Heeger points associated the genus class characters of real quadratic fields, do satisfy an analogue of the Gross-Zagier formula. This result has potential applications to understanding the class number one problem for certain class of real quadratic fields.
3. Dingxin Zhang, Jie Zhou, Twisted sectors in Calabi-Yau type Fermat polynomial singularities and automorphic forms, Communications in Number Theory and Physics Volume 19, Number 4, 683–744 (2025)
   Using mixed Hodge theory, this paper reveals a special arithmetic property of the solution spaces of the deformation differential equations for the twisted sectors of Calabi–Yau-type Fermat homogeneous singularities: via a particular coordinate transformation, the solutions to these differential equations can be identified with components of vector-valued automorphic forms for certain triangle groups. By means of mirror symmetry, the results of this paper imply the automorphy of the genus-zero Gromov–Witten generating functions for Fermat-type Calabi–Yau manifolds. Using differential Galois theory, the paper proves that the Yamaguchi–Yau ring, as a differential algebra, is generated by finitely many automorphic forms for a certain triangle group. This provides an affirmative answer to a question posed by Shing-Tung Yau in the early 2000s.
4. Yufan Luo, Some cases of the unramified Fontaine-Mazur conjecture, International Journal of Number Theory. Vol. 21, No. 05, pp. 1017-1027 (2025)
   This work applies Lazard’s theory of p-valuable pro-p groups to the study of the unramified Fontaine–Mazur conjecture in Galois representation theory, and verifies the conjecture in several important concrete cases. The paper effectively combines Lazard’s p-valuation theory, Koch’s explicit descriptions of Galois groups, and the theory of profinite groups, among other tools, thereby providing new affirmative examples and a group-theoretic framework of arguments for this fundamental conjecture.
5. Yufan Luo, Remarks on the Boston’s Unramified Fontaine-Mazur Conjecture, Journal of Number Theory, Volume 281, (2026), 96-109.
   This paper investigates the unramified Fontaine–Mazur–Boston conjecture in the theory of Galois representations. The first main result reduces the conjecture by proving that it suffices to verify it only for two special cases, namely for p-adic Galois representations and for F _p [[T]] -adic representations. The second main result establishes, under certain conditions, a finiteness theorem for the associated unramified Galois deformation rings.
6. Chung Pang Mok, Huimin Zheng, Monte Carlo Integration Using Elliptic Curves, Chinese Annals of Mathematics Series B, 46(2), 241–260, 2025.
   This work carries out numerical experiments with regard to the Monte Carlo integration method, using as input the pseudorandom vectors that are generated by the algorithm proposed in [Mok, C. P., Pseudorandom Vector Generation Using Elliptic Curves and Applications to Wiener Processes, Finite Fields and Their Applications, 85, 2023, 102129], which is based on the arithmetic theory of elliptic curves over finite fields. Two cases of integration are considered: the case of Lebesgue measure on the unit hypercube, and as well as the case of Wiener measure.
7. Chung Pang Mok, Huimin Zheng, Pseudorandomness of Sato-Tate Distributions for Elliptic Curves, Journal of Experimental Mathematics, 1(1):185–205, 2025.
   This work proposes conjectures that the Frobenius angles of a given elliptic curve over Q without complex multiplication is pseudorandom, in other words that the Frobenius angles are statistically independently distributed with respect to the Sato-Tate measure. Numerical evidence is presented to support the conjectures.

The team has achieved fruitful results in string theory, quantum field theory, and related mathematical fields. Professor Andrey Losev and others established the tropical Gromov–Witten theory for toric varieties and its precise correspondence with mirror symmetry (SIGMA 2024), and constructed combinatorial models for two-dimensional higher topological quantum field theories (Lett. Math. Phys. 2024). The team has also made a series of advances in cutting-edge directions such as celestial holography (Phys. Rev. D 2025), exact computations in superconformal field theories (JHEP 2025), and holographic principles (JHEP 2025).

Research Outputs

1. Oleksandr Gamayun, Andrei Losev, Mikhail Shifman, First-order formalism for β functions in bosonic sigma models from supersymmetry breaking, PHYSICAL REVIEW D 110, 025017 (2024).
   We consider the renormalization group flow equation for the two-dimensional sigma models with the Kähler target space. The first-order formulation allows us to treat perturbations in these models as Current-current deformations. We demonstrate, however, that the conventional first-order formalism misses certain anomalies in the measure, and should be amended. We reconcile beta functions obtained within the conformal perturbation theory for the current-current deformations with traditional “geometric” results obtained in the background field methods, in this way resolving the peculiarities pointed out in O. Gamayun et al. [Peculiarities of beta functions in sigma models, J. High Energy Phys. 10 (2023) 097]. The result is achieved by the supersymmetric completion of the first-order sigma model.
2. ZhengpingGui, SiLi, KeyouZeng, Quadratic duality for chiral algebras, Advances in Mathematics 451 (2024) 109791.
   We introduce a notion of quadratic duality for chiral algebras. This can be viewed as a chiral version of the usual quadratic duality for quadratic associative algebras. We study the relationship between this duality notion and the Maurer-Cartan equations for chiral algebras, which turns out to be parallel to the associative algebra case. We also present some explicit examples.
3. Andrey LOSEV, Vyacheslav LYSOV, Tropical Mirror, SIGMA 20 (2024), 072, 48.
   We describe the tropical curves in toric varieties and define the tropical Gromov–Witten invariants. We introduce amplitudes for the higher topological quantum mechanics (HTQM) on special trees and show that the amplitudes are equal to the tropical Gromov–Witten invariants. We show that the sum over the amplitudes in A-model HTQM equals the total amplitude in B-model HTQM, defined as a deformation of the A-model HTQM by the mirror superpotential. We derived the mirror superpotentials for the toric varieties and showed that they coincide with the superpotentials in the mirror Landau–Ginzburg theory. We construct the mirror dual states to the evaluation observables in the tropical Gromov–Witten theory.
4. A. S. Losev, T. V. Sulimov, MAURER–CARTAN METHODS IN PERTURBATIVE QUANTUM MECHANICS, Theoretical and Mathematical Physics, 221(3): 2155–2164 (2024).
   We reformulate the time-independent Schrödinger equation as a Maurer–Cartan equation on the superspace of eigensystems of the former equation. We then twist the differential such that its cohomology becomes the space of solutions with a fixed energy. A perturbation of the Hamiltonian corresponds to a deformation of the twisted differential, leading to a simple recursive relation for the eigenvalue and eigenfunction corrections.
5. Justin Beck, Andrey Losev, Pavel Mnev, COMBINATORIAL 2D HIGHER TOPOLOGICAL QUANTUM FIELD THEORY FROM A LOCAL CYCLIC A∞ ALGEBRA, Letters in Mathematical Physics 2024(125).
   We construct combinatorial analogs of 2d higher topological quantum field theories. We consider triangulations as vertices of a certain CW complex Ξ. In the “flip theory,” cells of Ξ_flip correspond to polygonal decompositions obtained by erasing the edges in a triangulation. These theories assign to a cobordism a cochain Z on Ξ_flip constructed as a contraction of structure tensors of a cyclic A_∞ algebra V assigned to polygons. The cyclic A_∞ equations imply the closedness equation (δ + Q)Z = 0. In this context we define combinatorial BV operators and give examples with coefficients in Z₂. In the “secondary polytope theory,” Ξ_sp is the secondary polytope (due to Gelfand-Kapranov-Zelevinsky) and the cyclic A_∞ algebra has to be replaced by an appropriate refinement that we call an Â_∞ algebra. We conjecture the existence of a good Pachner CW complex Ξ for any cobordism, whose local combinatorics is described by secondary polytopes and the homotopy type is that of Zwiebach’s moduli space of complex structures. Depending on this conjecture, one has an “ideal model” of combinatorial 2d HTQFT determined by a local Â_∞ algebra.
6. Ban Lin, Mauricio Romo, B-brane Transport and Grade Restriction Rule for Determinantal Varieties, Journal of High Energy Physics, 2024(268).
   We study autoequivalences of D^bCoh(X) associated to B-brane transport around loops in the stringy Kähler moduli of X. We consider the case of X being certain resolutions of determinantal varieties embedded in P^d×G(k, n). Such resolutions have been modeled, in general, by nonabelian gauged linear sigma models (GLSM). We use the GLSM construction to determine the window categories associated with B-brane transport between different geometric phases using the machinery of grade restriction rule and the hemisphere partition function. In the family of examples analyzed the monodromy around phase boundaries enjoy the interpretation as loop inside link complements. We exploit this interpretation to find a decomposition of autoequivalences into simpler spherical functors and we illustrate this in two examples of Calabi-Yau 3-folds X, modeled by an abelian and nonabelian GLSM respectively. In addition we also determine explicitly the action of the autoequivalences on the Grothendieck group K(X) (or equivalently, B-brane charges).
7. Hirotaka Hayashi, Tomoki Nosaka, Tadashi Okazaki, M2-M5 giant graviton expansions, Journal of High Energy Physics, 2024(109).
   We examine the giant graviton expansions of the Coulomb and Higgs indices for the M2-brane SCFTs to find the closed-form expressions for the indices that encode the spectra of the 1/4-BPS M5-brane giant gravitons and the 1/3-BPS orbifold M5-brane giant gravitons. Consequently, we get exact forms of the twisted indices for the 6d (2, 0) theories describing a stack of N M5-branes which generalize the unrefined indices. We confirm that they are also beautifully expanded with respect to the indices for the M2-brane giant gravitons which are obtained from the Coulomb and Higgs indices for the M2-brane SCFTs upon the change of variables.
8. Reiko Liu, Wen-Jie Ma, Celestial optical theorem, PHYSICAL REVIEW D 111, 025017 (2025).
   We derive the celestial optical theorem from the S-matrix unitarity, which provides nonperturbative bootstrap equations of conformal partial wave (CPW) coefficients. This theorem implies that the imaginary parts of CPW coefficients exhibit a positivity property. By making certain analyticity assumptions and using the celestial optical theorem, we derive nonperturbative constraints concerning the analytic structure of CPW coefficients. We discover that the CPW coefficients of four massless particles must and can only have simple poles located at specific positions. The CPW coefficients involving massive particles exhibit double-trace poles, indicating the existence of double-trace operators in nonperturbative celestial conformal field theory. It is worth noting that, in contrast to AdS/CFT, the conformal dimensions of double-trace operators do not have anomalous dimensions.
9. Reiko Liu, Wen-Jie Ma, Massive celestial amplitudes and celestial amplitudes beyond four points, Journal of High Energy Physics, 2025(180).
   We compute scalar three-point celestial amplitudes involving two and three massive scalars. The three-point coefficient of celestial amplitudes with two massive scalars contains a hypergeometric function, and the one with three massive scalars can be represented as a triple Mellin-Barnes integral. Using these three-point celestial amplitudes, we investigate the conformal block expansions of five- and six-point scalar celestial amplitudes in the comb channel. We observe the presence of two-particle operators in the conformal block expansion of five-point celestial amplitudes, which confirms the previous analysis by taking multi-collinear limit. Moreover, we find that there are new three-particle operators in the conformal block expansion of six-point celestial amplitudes. Based on these findings, we conjecture that exchanges of n-particle operators can be observed by considering the comb channel conformal block expansion of (n + 3)-point massless celestial amplitudes. Finally, we show that a new series of operators appears when turning on the mass of the first incoming particle. The leading operator in this series can be interpreted as a two-particle exchange in the OPE of one massive and one massless scalars.
10. Naotaka Kubo, Tomoki Nosaka, Yi Pang, Exact large N expansion of mass deformed ABJM theory on squashed sphere, Journal of High Energy Physics, 2025(2), 1-31.
    In this paper we study the partition function of the mass deformed ABJM theoryon a squashed three sphere. In particular, we focus on the case with the Chern-Simons levels being +1 or -1, and apply a duality between this theory and the N = 4 U(N) super Yang-Mills theory with an adjoint hypermultiplet and a fundamental hypermultiplet. For a special mass parameter depending on the squashing parameter, we find that the partition function can be written as that of an ideal Fermi gas with a non-trivial density matrix. By studying this density matrix, we analytically derive the all order perturbative expansion of the partition function in 1/N, which turns out to take the form of the Airy function. Our results not only align with previous findings and conjectures but also lead to a new formula for the overall constant factor of the partition function. We also study the exact values of the partition function for small but finite values of N.
11. Hongfei Shu, Peng Zhao, Rui-Dong Zhu, Hao Zou, Counting Bethe states in twisted spin chains, Journal of High Energy Physics, 2025(87).
    We present a counting formula that relates the number of physical Bethe states of integrable models with a twisted boundary condition to the number of states in the untwisted or partially twisted limit.
12. Wei Gu, Leonardo Mihalcea, Eric Sharpe, Hao Zou, Quantum K theory of Grassmannians,Wilson line operatorsand Schur bundles, Forum of Mathematics, Sigma (2025), Vol. 13:e140 1–38.
    We prove a ‘Whitney’ presentation, and a ‘Coulomb branch’ presentation, for the torus equivariant quantum K theory of the Grassmann manifold Gr(k;n), inspired from physics, and stated in an earlier paper. The first presentation is obtained by quantum deforming the product of the Hirzebruch λ_y classes of the tautological bundles. In physics, the λ_y classes arise as certain Wilson line operators. The second presentation is obtained from the Coulomb branch equations involving the partial derivatives of a twisted superpotential from supersymmetric gauge theory. This is closest to a presentation obtained by Gorbounov and Korff, utilizing integrable systems techniques. Algebraically, we relate the Coulomb andWhitney presentations utilizing transition matrices from the (equivariant) Grothendieck polynomials to the (equivariant) complete homogeneous symmetric polynomials. Along the way, we calculate K-theoretic Gromov-Witten invariants of wedge powers of the tautological bundles on Gr(k;n), using the ‘quantum=classical’ statement.
13. Wei Gu, Leonardo Mihalcea, Eric Sharpe, Weihong Xu, Hao Zhang, Hao Zou, Schubert defects in Lagrangian Grassmannians, Journal of High Energy Physics, 2025(148).
    In this paper, we propose a construction of GLSM defects corresponding to Schubert cycles in Lagrangian Grassmannians, following recent work of Closset-Khlaif on Schubert cycles in ordinary Grassmannians. In the case of Lagrangian Grassmannians, there are superpotential terms in both the bulk GLSM as well as on the defect itself, enforcing isotropy constraints. We check our construction by comparing the locus on which the GLSM defect is supported to mathematical descriptions, checking dimensions, and perhaps most importantly, comparing defect indices to known and expected polynomial invariants of the Schubert cycles in quantum cohomology and quantum K theory.
14. Chen Yuan, Yizhou Lu, Zu-Cheng Chen, Lang Liu, On the gauge invariance of secondary gravitational waves, JCAP07 2025016.
    Second-order tensor perturbations induced by primordial fluctuations play a crucial role in probing small-scale physics, but gauge dependence of their energy density has remained a fundamental challenge in cosmological perturbation theory. We address this issue by introducing a boundary condition-based filtering method that extracts physical radiation through the Sommerfeld criterion. We demonstrate that after filtering non-physical modes, the energy density of secondary gravitational waves becomes gauge-invariant and exhibits physically consistent behavior in the sub. horizon limit. This approach provides a unified framework for both adiabatic and isocurvature perturbations, enhancing theoretical predictions and observational signatures of earl universe physics.
15. Naotaka Kubo, Tomoki Nosaka, Yi Pang, Exact large N expansion of N = 4 circular quiver Chern-Simons theories, PHYSICAL REVIEW D 112, 046023 (2025).
    In this work, we revisit the exact computation of the round sphere partition function of 3d N=4 circular quiver Chern-Simons theories with mass and Fayet-Iliopoulos (FI) deformations. Utilizing the Fermi gas formalism, we derive the large N expansion of the partition function and determine the Airy function structure, parameterized by three functions C, B, and A. We propose a novel closed-form expression for A that incorporates the effects of FI parameters and satisfies various consistency constraints from quiver reductions. As an application, by using an accidental coincidence of the Fermi gas density matrices we extend our results to the squashed sphere partition function of N=4 super Yang-Mills theories with an adjoint hypermultiplet and multiple fundamental hypermultiplets. Our findings provide further evidence for the universality of the Airy function structure in supersymmetric gauge theories of multiple M2-branes.
16. George Georgiou, Georgios Linardopoulos, Dimitrios Zoakos, Holography of a novel codimension-2 defect CFT, Journal of High Energy Physics, 2025(105).
    We propose and study a new holographic duality between a non-supersymmetric defect conformal field theory (dCFT) and its gravity dual. On the gravity side, the defect is realised by a novel solution of a D5 probe brane embedded in the AdS₅×S⁵ geometry. The D5 brane wraps an S² ⊂ S⁵ and carries k units of flux through the S². The symmetry of the induced on the brane metric is AdS₃×S¹×S². The brane ends on an R^(1,1) subspace of the 4-dimensional AdS₅ boundary resulting to a codimension-2 defect. We first prove that our brane configuration is stable by showing that the masses of all the fluctuations of the transverse to the brane coordinates respect the B-F bound. On the field theory side, the 2-dimensional defect is described by a classical solution whose precise form we determine. Subsequently, we calculate the one-point functions of the energy-momentum tensor and of the chiral primary operators (CPOs), first at strong and then at weak coupling. In an appropriate limit, we find compelling agreement between the weak and strong coupling results. Furthermore, we also extract one of the B-type Weyl anomaly coefficients.
17. Hirotaka Hayashi, Tomoki Nosaka, Tadashi Okazaki, Abelian dualities and line defect indices for 3d gauge theories, Journal of High Energy Physics, 2025(177).
    We find matching pairs of the line defect indices for 3d supersymmetric Abelian gauge theories as strong evidence of dualities of the BPS line operators. They lead to novel duality maps of the BPS line operators for N ≥ 4 supersymmetric circular and linear quiver gauge theories which can be realized as brane configurations in Type IIB string theory, including SQED, ADHM and ABJM theories.
18. Sebastian Garcia-Saenz, Yizhou Lu, Sébastien Renaux-Petel, Loops in inflation with strongly non-geodesic motion, JCAP11(2025)039.
    We study loop corrections in the effective field theory of inflation with imaginary speed of sound, which has been shown to provide an effective description of multi-field inflationary models characterized by strongly non-geodesic motion and heavy entropic perturbations. We focus on the one-loop corrections to the scalar and tensor power spectra, taking into account all relevant vertices at leading order in derivatives and in slow-roll. We find a power-law dependence of the scalar two-point function on the scale that defines the range of validity of the effective theory, analogous to the enhancement observed in tree-level correlation functions. Even more dramatic, the relative correction to the tensor spectrum is exponentially enhanced, albeit also suppressed in the slow-roll limit. In spite of these large effects, our results show that this class of models can satisfy the requirement of perturbative control and a consistent loop expansion within a range of parameters of phenomenological interest. On the other hand, models predicting large values of the power spectrum on small scales are found to be under strong tension. As a technical bonus, we carefully explain the prescription for the regularization and manipulation of loop integrals in this set-up, where one has a non-trivial domain of integration for time and momentum integrals owing to the regime of validity of the effective field theory. This procedure is general enough to be of potential applicability in other contexts.
19. Mikhail Litvinov, Sergey Alekseev, Mykola Dedushenko, Chiral life on a slab, Letters in Mathematical Physics (2026) 116:7.
    We study chiral algebra in the reduction of 3D N = 2 supersymmetric gauge theories on an interval with the N = (0, 2) Dirichlet boundary conditions on both ends. By invoking the 3D “twisted formalism” and the 2D βγ -description, we explicitly find the perturbative $\bar{\bf{Q}}_{+}$ cohomology of the reduced theory. It is shown that the vertex algebras of boundary operators are enhanced by the line operators. A full non-perturbative result is found in the abelian case, where the chiral algebra is given by the rank two Narain lattice VOA, and two more equivalent descriptions are provided. Conjectures and speculations on the non-perturbative answer in the non-abelian case are also given.
20. Guorui Ma, Stephen S.-T. Yau, Huaiqing Zuo, On (k,l)-th singular locus moduli algebras of singularities and their derivation Lie algebras, Journal of Algebra 685 (2026) 673-688.
    This paper introduces a series of new invariants to study singularity problems. We propose a conjecture that for weighted homogeneous isolated hypersurface singularities, the newly defined (k,l)-singularity trajectory module algebra admits no negative-weight derivations. This conjecture is verified in several cases.
21. B. Lian, K. Spinelli, Restriction theorems: from orbits and Chevalley to periods andonsGalois, submitted 2025.
    Using a new approach based on Galois theory, we study subvarieties of complex representations of reductive groups which satisfy restriction properties on their invariant rings and function fields, along the lines of the Chevalley restriction theorem. For a certain well-behaved class of representations, we explicitly parametrize candidates for these restriction properties and explain a technique to understand their deformations in complex families. We also give algebraic and geometric characterizations of the Chevalley restriction property which clarify how this perspective connects back to previous orbit-theoretic approaches. Finally, we utilize these restriction properties to prove explicit formulas for period integrals of some Calabi-Yau families. The key insight is that the restriction property on function fields can be leveraged to locally interpolate between the algebraic and analytic settings. Using this technique, we lift hypergeometric period formulas from subfamilies to obtain novel explicit formulas for periods of Calabi-Yau double covers of projective spaces and elliptic curves in \mathbb{P}^2, expressed in terms of invariant functions on their parameter spaces.
22. T.J. Lee, B. Lian, S-T. Yau, Mirror Symmetry for Double Cover Calabi-Yau Varieties II., submitted 2025.
    The presented paper is a continuation of the series of papers arXiv:1810.00606 and arXiv:1903.09373. In this paper, utilizing Batyrev and Borisov’s duality construction on nef-partitions, we generalize the recipe in arXiv:1810.00606 and arXiv:1903.09373 to construct a pair of singular double cover Calabi–Yau varieties $(Y, Y^\vee)$ over toric manifolds and compute their topological Euler characteristics and Hodge numbers. In the 3-dimensional cases, we show that $(Y, Y^\vee)$ forms a topological mirror pair, i.e., $ h^{p,q}(Y) = h^{3-p,q}(Y^\vee) $ for all $p, q$.
23. T.J. Lee, B. Lian, M. Romo, L. Santilli, Non-commutative resolutions and pre-quotients of Calabi-Yau double covers, submitted 2025.
    Following an earlier proposal arXiv:2307.02038 to apply the GLSM formalism to understand the so-called non-commutative resolution, this paper takes one important step further to extend this formalism to a much larger class of non-commutative resolutions. The proposal was initially motivated by the discovery of a new class of mirror pairs singular Calabi-Yau varieties arXiv:2003.07148, given by certain branched double covers over toric varieties of MPCP type. The overarching problem was to understand these mirror pairs from the viewpoint of homological mirror symmetry arXiv:alg-geom/9411018. In the present paper, we propose two main results along this line. First, one new insight is that the ‘gauge-fixing’ condition on the branching locus of the double cover used in arXiv:2003.07148 can be relaxed in an interesting way. This turns out to produce GLSMs that describe a much larger class of non-commutative resolutions, leading to A-periods for a larger class of non-commutative resolutions, as well as the GKZ systems for their A-periods. Second, we show that the A-periods can also be realized as A-periods of a certain smooth CICY family in a toric variety of MPCP type, such that a suitable finite quotient of this family recovers the double cover CY we have started with. We call this CICY family the ‘pre-quotient’ of the double cover CY. This realization strongly suggests that pre-quotient may provide an important approach for understanding homological mirror symmetry for singular double cover CY varieties and non-commutative resolutions.
24. T.J. Lee, B. Lian, M. Romo, Non-commutative resolutions as mirrors of singular Calabi-Yau varieties, submitted 2025.
    It has been conjectured that the hemisphere partition function arXiv:1308.2217, arXiv:1308.2438 in a gauged linear sigma model (GLSM) computes the central charge arXiv:math/0212237 of an object in the bounded derived category of coherent sheaves for Calabi–Yau (CY) manifolds. There is also evidence in arXiv:alg-geom/ 9511001, arXiv:hep-th/0007071. On the other hand, non-commutative resolutions of singular CY varieties have been studied in the context of abelian GLSMs arXiv:0709.3855. In this paper, we study an analogous construction of abelian GLSMs for non-commutative resolutions and propose they can be used to study a class of recently discovered mirror pairs of singular CY varieties. Our main result shows that the hemisphere partition functions (a.k.a.~ -periods) in the new GLSM are in fact period integrals (a.k.a.~ -periods) of the singular CY varieties. We conjecture that the two are completely equivalent: -periods are the same as -periods. We give some examples to support this conjecture and formulate some expected homological mirror symmetry (HMS) relation between the GLSM theory and the CY. As shown in arXiv:2003.07148, the -periods in this case are precisely given by a certain fractional version of the -series of arXiv:alg-geom/9511001. Since a hemisphere partition function is defined as a contour integral in a cone in the complexified secondary fan (or FI-theta parameter space) arXiv:1308.2438, it can be reduced to a sum of residues (by theorems of Passare-Tsikh-Zhdanov and Tsikh-Zhdanov). Our conjecture shows that this residue sum may now be amenable to computations in terms of the -series.
25. T.J. Lee, B. Lian, S-T. Yau, On Calabi-Yau fractional complete intersections, Pure and applied mathematics quarterly, 18, 1, 317- 342.
    In this article, we study mirror symmetry for pairs of singular Calabi–Yau manifolds which are double covers of toric manifolds. Their period integrals can be seen as certain `fractional’ analogues of those of ordinary complete intersections. This new structure can then be used to solve their Riemann–Hilbert problems. The latter can then be used to answer definitively questions about mirror symmetry for this class of Calabi–Yau manifolds.

The team has achieved milestone results in operator algebras and quantum measurement. Professor Huaxin Lin successfully resolved a quantum measurement problem raised by the renowned mathematician David Mumford, rigorously proving the existence of “asymptotically macroscopically unique states” (Commun. Math. Phys. 2025). He has also made significant progress toward proving the Toms–Winter conjecture, a central problem in the classification of C*-algebras (J. Funct. Anal. 2025). Furthermore, the team has also advanced research on the Novikov conjecture in higher index theory (J. Funct. Anal. 2025).

Research Outputs

1. Huaxin Lin, Existence of Approximately Macroscopically Unique States, Commun. Math. Phys., 406 (2), Paper No. 38, 17 pp., 2025.
   This paper aims to answer a fundamental question about quantum mechanics raised by David Mumford. At the end of his opening lecture, “Consciousness, robots and DNA,” at the inaugural International Congress of Basic Science (ICBS) in 2023, Mumford asked whether “Approximately Macroscopically Unique” (AMU) states exist when macroscopic observables almost commute. These states describe a world recognizable to us with no “maybe dead/maybe alive” cats. This work provides an affirmative answer. Notably, Mumford envisioned constructing such states by approximating the quantum variables with commuting ones. This paper points out the existence of situations where certain almost commuting macroscopic observables cannot be approximated by commuting operators, and proves the existence of AMU states even in such cases.
2. Huaxin Lin, Strict comparison and stable rank one, J. Funct. Anal. 289 (2025), no. 9, Paper No. 111065, 25 pp.
   The Toms-Winter conjecture is an important problem in the classification program of C*-algebras. The conjecture states that simple, separable, amenable C*-algebras with strict comparison are Z-stable. It is known that Z-stability implies stable rank one and the surjectivity of the rank map. However, it has remained unknown whether strict comparison alone could guarantee the stable rank one, much less Z-stability. This paper achieves a major breakthrough on this issue: for a σ-unital finite simple C*-algebra, strict comparison combined with the surjectivity of the rank map indeed implies stable rank one. Furthermore, the author also obtains the dichotomy that simple pure C∗-algebras are either purely infinite or have stable rank one. This dichotomy advances the Toms-Winter conjecture by proving that pureness – a property implied by Z-stability – already enforces stable rank one, independent of amenability or exactness.
3. George A. Elliott, Guihua Gong, Huaxin Lin, Zhuang Niu, On the classification of simple amenable C* algebras with finite decomposition rank, II, J. Noncommut. Geom. 19 (2025), no. 1, 73–104.
   This paper proves that if a unital, simple, separable C*-algebra has finite decomposition rank and satisfies the Universal Coefficient Theorem (UCT), then the tensor product of this algebra with the universal UHF algebra has generalized tracial rank at most one. Consequently, such an algebra is classifiable by the Elliott invariant.
4. Jintao Deng, Liang Guo, Qin Wang, Guoliang Yu, Higher index theory for spaces with an FCE-by-FCE structure, J. Funct. Anal. 288 (2025), no. 1, Paper No. 110679, 49 pp.
   The coarse Novikov conjecture stands as one of the central conjectures in higher index theory and non-commutative geometry; its validity resolves the conjecture regarding obstructions to positive scalar curvature on aspherical manifolds. This paper introduces an “FCE-by-FCE” structure for metric spaces. In particular, for a sequence of extensions of finite groups, if the sequence of normal subgroups and the sequence of quotient groups both admit a fibred coarse embedding into Hilbert space, then this extension sequence possesses the “FCE-by-FCE” structure. In their 2015 work, Arzhantseva and Tessera proved that such extension sequences generally do not admit a fibred coarse embedding into Hilbert space, leaving the higher index problem for such spaces unresolved. This paper proves that the coarse Novikov conjecture holds for such spaces and simultaneously proves that they possess boundary coarse K-amenability
5. Huaxin Lin, Double duals and Hilbert modules, Anal. PDE., 18 (2025), no. 6, 1531–1566.
   This paper studies Hilbert C*-modules and the double dual structure of C*-algebras. For any C*-algebra A and any Hilbert A-module H, the W*-algebra of bounded A**-module maps on the smallest self-dual Hilbert A**-module containing H is isomorphic to K(H)**. Furthermore, it is proved that the unit ball of H is dense in the weak *-topology of H^# and closed in the A-weak topology induced by H^#, where H^# is the dual module of H. The paper also establishes a version of Kaplansky’s density theorem for Hilbert C*-modules.
6. Xuanlong Fu, Huaxin Lin, Tracial oscillation zero and stable rank one, Canad. J. Math. 77 (2025), no. 2, 563–630.
   This paper proves that, for a separable simple C*-algebra with strict comparison, the following three properties are equivalent: having tracial approximate oscillation zero, having stable rank one, and having a surjective canonical map Γ on its Cuntz semigroup. Consequently, it is shown that if a separable simple C*-algebra with strict comparison and surjective Γ has almost stable rank one, then it must have stable rank one.
7. Lawrence G. Brown, Huaxin Lin, Projective Hilbert modules and sequential approximations, Sci. China Math. 68(2025), 137–168.
   This paper proved that for any separable C*-algebra, all its countably generated Hilbert modules are projective. The paper also examines the approximate extension problem for bounded module maps, establishing that every countably generated Hilbert module is both “approximately injective” and “approximately projective”. Furthermore, under the additional assumptions that the C*-algebra has strict comparison and its canonical rank map Γ is surjective, a classification theorem is provided: the countably generated Hilbert modules can be fully classified by affine lower semicontinuous functions on the quasitrace space if and only if this algebra has stable rank one.

The team has developed a series of efficient algorithms to successfully tackle significant application challenges. Proposing the fast algorithm FAME: Efficiently solves the band structure of 3D photonic crystals, significantly outperforming commercial software (SIAM J. Sci. Comput. 2024). Innovatively integrating Optimal Transport with Tensor SVD: Constructed a deep learning model for brain tumor image segmentation and molecular typing, achieving performance superior to that of senior experts (PNAS 2025). Proposing a multi-block ADMM algorithm: Successfully addressed the non-convex optimization challenge in nonlinear climate data assimilation (J. Comput. Phys. 2025).

Research Outputs

1. Z.-H. Tan, T. Li, W.-W. Lin and S.-T. Yau, n-Dimensional Volumetric Stretch Energy Minimization for Volume-/Mass-Preserving Parametrizations with Applications, SIAM Journal on Imaging Sciences, 18.2, (2025), 1141-1175.
   Based on the n-dimensional Dirichlet energy, this paper defines the n-dimensional Volume Stretching Energy (n-VSE) on an n-dimensional manifold M, covering both continuous and discrete cases. The discrete n-VSE can be represented by a cotangent-weighted Laplacian matrix, which subsumes the previously proposed volume stretching energy as special cases when n=2 and n=3. We propose an n-VSEM algorithm for computing the volume/mass-preserving parameterization between M and the unit n-sphere. The n-VSEM algorithm for M is decomposed into two subproblems: a small-scale constrained boundary subproblem, which is solved via Newton iteration combined with the trust region method; and a large-scale unconstrained interior subproblem, which is addressed using fixed-point iteration. Numerical experiments demonstrate the accuracy and robustness of the proposed algorithm. In addition, the improved n-VSEM algorithm can be applied to manifold registration and deformation, indicating the versatility of the n-VSEM algorithm.
2. B. Li, B. Shi. Numerical Solution for Nonlinear 4D Variational Data Assimilation (4D-Var) via ADMM, Journal of Computational Physics, 538:114163, 2025.
   This paper innovatively proposes a multi-module ADMM algorithm for solving the variational data assimilation problem in nonlinear dynamical systems. The core breakthrough of this method lies in its abandonment of the strict requirement for satisfying dynamical constraints in traditional methods for the highly nonconvex variational objective function derived from the initial conditions of the nonlinear dynamical system. Instead, it allows the solution to be optimized near the dynamical equations, thus enabling simultaneous solution of the dynamical trajectory over the entire time span. This strategy effectively avoids the inherent defect of classical gradient-based algorithms that are prone to getting trapped in undesirable local minima, significantly improving the robustness and global optimization capability of the solution.
3. Z. Zhu, H. Wang, T. Li, T.-M. Huang, H. Yang, Z. Tao, J. Zhou, S. Chen, Z.-H. Tan, M. Ye, Z. Zhang, F. Li, D. Liu, J. Lu, W. Zhang, X. Li, Q. Chen, Z. Jiang, F. Chen, X. Zhang, W.-W. Lin, S.-T. Yau, B. Zhang, OMT and tensor SVD based deep learning model for segmentation and predicting genetic markers of glioma: a multicenter study, Proceedings of the National Academy of Sciences of the United States of America, 122.28 (2025), e2500004122.
   This study employs deep learning models to segment tumor regions and predict the World Health Organization (WHO) grade, isocitrate dehydrogenase (IDH) mutation status, and 1p/19q codeletion status based on preoperative magnetic resonance imaging (MRI) data. To achieve accurate tumor segmentation, we developed an optimal mass transport (OMT) method that transforms irregular brain MRI images into tensors. Furthermore, we proposed an algebraic pre-classification (APC) model, which leverages singular value decomposition (SVD) of multi-modal OMT tensors to estimate pre-classification probabilities. A fully automated deep learning model named OMT-APC was utilized for multi-task classification in this work. Evaluated on The Cancer Genome Atlas (TCGA) dataset, the OMT-APC model achieved an accuracy of 0.855, 0.917, and 0.809, as well as an area under the curve (AUC) of 0.845, 0.908, and 0.769 for predicting WHO grade, IDH mutation status, and 1p/19q codeletion status, respectively. The model outperformed four board-certified radiologists across all tasks. These results highlight the efficacy of our OMT- and tensor SVD-based approach for the genomic profiling of brain tumors, demonstrating the broad application prospects of algebraic and geometric methods in medical image analysis.
4. X. Zeng, B. Shi. A Lyapunov Analysis of Accelerated PDHG Algorithms, Journal of Global Optimization, 207(67):1-20 2025.
   The contribution of this paper lies in proposing a novel Lyapunov function and using it to rigorously prove the convergence rate of the accelerated PDHG (Primitive-Dual Hybrid Gradient) algorithm. Furthermore, this research reveals and points out the “displaced multiplication” structural feature exhibited by the accelerated PDHG algorithm during the iteration process, providing a new theoretical perspective for understanding the algorithm’s intrinsic mechanism.
5. X.-L. Lyu, T. Li, J.-W. Lin and W.-W. Lin, An SVD-based Fast Algorithm for 3D Maxwell’s Equations with Perfect Electric Conductor and Quasi-periodic Boundary Conditions. SIAM Journal on Scientific Computing, 46. 6, (2024), B925-B952.
   This paper proposes a fast algorithm, FAME, for computing the band structures of three-dimensional photonic crystals with supercell architectures and hybrid boundary conditions of perfect electrical conductors and quasi-periodicity. We discretize the frequency-domain source-free Maxwell’s equations using the skewed Yee finite-difference method, with uniform discretization implemented for different Bravais lattices. By leveraging the singular value decomposition (SVD) of discrete differential operators along each direction, we derive an explicit SVD of the discrete curl operator, which inherently incorporates the fast Fourier transform (FFT) structure. With the aid of the explicit basis of the range space embedded in the SVD of the discrete curl operator, we transform the Maxwell eigenvalue problem into a generalized eigenvalue problem free of null space, which can be directly solved via the conjugate gradient method. In each matrix-vector multiplication, the discrete cosine/sine transform operations induced by the perfect electrical conductor boundary conditions, as well as the quasi-periodic boundary conditions, can be accelerated by the fast Fourier transform (FFT) with a computational complexity of O(NlogN). Numerical experiments verify the effectiveness of FAME and realize the surface state phenomenon in three-dimensional photonic crystals with helical supercell architectures.
6. H. Yang, Z. Zhu, L. Zhou, J. Zhou, Z. Tao, X. Wu, C. Tian, D. Liu, L. Wei, H. Wang, Z. Zhao, Y. Zhu, X. Wang, T. Li, W.-W. Lin, Y. Dai, X. Zhang and B. Zhang, Clinical and VASARI Features to Predict CDKN2A/B Homozygous Deletion in IDH-Mutant Astrocytomas: A Multicenter Study, American Journal of Neuroradiology, 46.10 (2025):2107-2115.
   Based on clinical characteristics and Visually Accessible Rembrandt Images (VASARI) MRI features, this study constructed and validated a predictive model for identifying the homozygous deletion status of CDKN2A/B in IDH-mutant astrocytoma. The optimal cutoff value of the nomogram, calculated using the Youden index, was determined to be 124.20 points. At this cutoff value, the predictive model achieved an accuracy of 85%, sensitivity of 67%, and specificity of 88% in the training cohort; in the external validation cohort, the corresponding values were 83%, 75%, and 86%, respectively.
7. T.-M. Huang, Y.-C. Kuo, R.-C. Li and W.-W. Lin, Numerical Solutions for Stochastic Continuous-time Algebraic Riccati Equations, SIAM Journal on Matrix Analysis and Applications, 46.3 (2025), 1675-1700.
   This paper investigates efficient numerical methods for the stochastic continuous-time algebraic Riccati equation (SCARE). Such equations typically arise from the state-dependent Riccati equation approach, which is arguably the only systematic methodology currently available for addressing nonlinear control problems. In this work, we revisit the application of Newton’s method to SCARE, with a primary focus on enhancing the practicality of Newton’s method. Finally, numerical experiments are conducted to verify the robustness of the proposed new method as well as the robust implementation of Newton’s method.
8. Q. Liu, T. Li, W.-W. Lin and S. Zhang, A Mix Finite Element Scheme for Three-dimensional Maxwell’s Transmission Eigenvalue Problems, Inverse Problems, 41 (2025), 045012, 1-25.
   This paper presents an efficient numerical method for solving the Maxwell transmission eigenvalue problem in three-dimensional domains where the first Betti number is zero. To this end, we introduce several auxiliary variables to reduce the order of the fourth-order problem, ultimately deriving an equivalent and stable linear eigenvalue problem with a compact operator. By applying a mixed finite element formulation, we obtain a sparse generalized eigenvalue problem (GEP), which does not introduce any spurious eigenvalues and achieves the optimal convergence rate for eigenvalues. Furthermore, we precondition all eigenvalues while preserving the sparse matrix multiplication structure, thereby deriving the final GEP. Based on the preconditioning results, we develop a multigrid-type block Jacobi-Davidson method for computing several smallest positive real Maxwell transmission eigenvalues. Extensive numerical examples demonstrate the effectiveness and efficiency of the proposed method.
9. X.-L. Lyu, T. Li and W.-W. Lin, A Contour Integral-Based Method for Nonlinear Eigenvalue Problems for Semi-Infinite Photonic Crystals, Computer Physics Communications, 306, (2025), 109377.
   This study proposes an efficient method for identifying the isolated exceptional points of two-dimensional semi-infinite and bi-infinite photonic crystals with hybrid boundary conditions of perfect electrical conductors and quasi-periodicity. The problem can be modeled by the Helmholtz equation and reformulated as a generalized eigenvalue problem involving infinite-dimensional block quasi-Toeplitz matrices. By skillfully implementing a matrix transformation that preserves the cyclic structure, we apply the contour integral method to compute the isolated eigenvalues and extract one component of the associated eigenvectors. Furthermore, we derive a propagation formula for electromagnetic fields. This formula enables the rapid calculation of field distributions in extended semi-infinite and bi-infinite domains, thereby highlighting the characteristics of edge states.
10. Z.-H. Tan, T. Li, W.-W. Lin and S.-T. Yau, A Robust Hessian-based Trust Region Algorithm for Spherical Conformal Parameterizations. Science China Mathematics, 68. 6, (2025), 1461-1486.
    Surface parameterization is widely applied in computer graphics, medical imaging, transformation optics, and other fields. In this paper, we rigorously derive the gradient vector and Hessian matrix of the discrete conformal energy for spherical conformal parameterization of closed, simply-connected surfaces with zero genus. Furthermore, we present the sparse structure of the Hessian matrix and, based on this, propose a robust trust-region algorithm that leverages the Hessian matrix to compute spherical conformal mappings. Numerical experiments demonstrate that the proposed algorithm achieves local quadratic convergence with low conformal distortion. Subsequently, we apply this method to surface registration and verify its local quadratic convergence property.
11. T. Li, L.O. Jolaoso, M. Adegoke, Y. Shehu and J.C. Yao, Training of Extreme Learning Machine Network Based on Novel Generalized Inertial Forward-reflected-backward Splitting Algorithm, Optimization, 74. 17, (2025), 4497–4516.
    This paper proposes a novel generalized inertial forward-reflected-backward splitting algorithm (IRFBA) for solving monotone inclusion problems involving three operators in real Hilbert spaces. We introduce a new double inertial extrapolation step, which enhances the acceleration performance of the splitting algorithm and achieves a trade-off between the parameters of the inertial step. Unlike existing literature, the proposed method does not require prior estimation of the Lipschitz constants of the operators in the additive terms. Subsequently, we investigate the weak convergence and linear convergence of the method under mild conditions. We validate the performance of the proposed IRFBA using real-world machine learning datasets. To evaluate its effectiveness, we compare our algorithm with three other state-of-the-art training algorithms. For the comparison, we construct regression problems based on the concept of extreme learning machines and conduct multiple experiments to comprehensively test the robustness of the IRFBA. Analyses of various metrics—including mean squared error (MSE), coefficient of determination R2??? , mean absolute error (MAE), root mean squared error (RMSE), and convergence rate—consistently demonstrate the high efficiency of the proposed IRFBA.
12. H. Liu, W. Zheng, L. Qin, J. Feng and T. Li, Aerodynamic Nonlinear Modeling and Body-Freedom Flutter Suppression of Flying-Wing Aircraft, Journal of Aircraft, 62.5, (2025), 1424–1432.
    To address the body freedom flutter problem of blended-wing-body (BWB) aircraft, it is crucial to develop a highly robust active flutter suppression method. This paper proposes an active flutter suppression scheme based on robust control theory for solving the body freedom flutter suppression problem of BWB aircraft. First, a novel aero-servo-elastic modeling framework for BWB aircraft is presented. By improving the vortex lattice method (VLM) and incorporating aerodynamic nonlinear effects into the aerodynamic calculation part of the model, the accuracy of flutter velocity calculation is enhanced. Then, based on this model, a robust active flutter suppression method is proposed using loop-shaping theory. Through optimizing the design of the generalized system, this method avoids the coupling between controller inputs and the high-low frequency dynamic characteristics, and improves the design of weight factors, thereby reducing the difficulty of parameter tuning. Finally, the stability and robustness of the closed-loop system are analyzed via time-domain and frequency-domain experiments. Simulation results demonstrate that the proposed control method can significantly expand the flutter velocity boundary of BWB aircraft, while maintaining sufficient stability margins and strong robustness.
13. B. Tan, Y. Shehu, T. Li and X. Qin, Perturbed Reflected Forward Backward Splitting Algorithm for Monotone Inclusion, Communications in Nonlinear Science and Numerical Simulation, 142, (2025),108565.
    This paper investigates a novel reflected forward-backward splitting algorithm with an adaptive step size for solving monotone inclusion problems. Unlike existing reflected forward-backward splitting algorithms, the implementation of the proposed algorithm does not require prior knowledge of the Lipschitz constant of the Lipschitz-continuous monotone operator. Under standard conditions, we establish a weak convergence theorem for the proposed algorithm. By applying the algorithm to signal processing and image deblurring tasks, we conduct a numerical comparison of its performance against that of other relevant algorithms reported in the literature.
14. Z. Yang, B. Zheng, T. Li, A Structure-preserving Method for the Total Least Squares Problems in Quaternionic Quantum Theory, Journal of Nonlinear and Convex Analysis, 26. 3, (2025), 577-589.
    This paper investigates the quaternion total least squares (QTLS) problem and derives a structure-preserving bidiagonalization-based iterative algorithm using the real counterparts of quaternion matrices, which is designed to obtain approximate solutions to the QTLS problem in quaternion quantum theory. Our method is capable of yielding true quaternion TLS solutions. Numerical examples demonstrate that the proposed algorithm is numerically stable and exhibits superior performance.
15. Kaveh Hojjatollah Shokri, Masoud Hajarian, and Anthony T. Chronopoulos. Improving communication in conjugate gradient solvers using regularized variable s-step approach. Filomat. 39.34 (2025): 12167-12187.
    The conjugate gradient (CG) method is widely used to solve symmetric positive definite (SPD) linear systems arising from signal processing problems. Communication overhead exerts a significant impact on the performance of this algorithm. To address this issue, this paper proposes a communication-reduced algorithm for solving linear systems with single or multiple right-hand sides, which integrates the conjugate gradient method with the synergetic conjugate gradient method. Subsequently, the performance of the proposed algorithm is further enhanced by techniques such as adjusting the parameter s in the s-step algorithm and tuning the regularization parameter.
16. S. Chen, B. Shi, Y. Yuan. Revisiting Nesterov’s acceleration via high-resolution differential equations, Journal of Global Optimization, 93:551-569, 2025.
    This paper proposes a simplified gradient correction scheme for Lyapunov analysis and applies it systematically to prove the convergence of the Nesterov accelerated gradient method. By introducing an implicit velocity scheme, this work establishes a unified method for constructing Lyapunov functions, providing not only a concise and rigorous theoretical proof for the Nesterov accelerated gradient method, but also distilling it into a universally applicable methodological principle, offering a clear theoretical tool for analyzing a class of accelerated optimization algorithms.
17. B. Li, B. Shi, Y. Yuan. Proximal Subgradient Norm Minimization of ISTA and FISTA, Applied and Computational Harmonic Analysis, 82:101848, 2026.
    The core contribution of this paper lies in its fundamental improvement of the basic gradient inequality, which systematically extends the Lyapunov analysis framework, originally applicable only to smooth optimization problems, to optimization problems containing non-smooth composite terms (such as image denoising). Furthermore, this research is the first to theoretically reveal and prove that the proximal gradient method possesses accelerated convergence properties, and numerical experiments demonstrate that this accelerated method has superior practical effectiveness and computational efficiency compared to traditional methods when solving real-world problems.
18. S. Wang, K. Gai, S. Zhang. Progressive Feedforward Collapse of ResNet Training, IEEE Transactions on Neural Networks and Learning Systems, 2025.
    This paper systematically characterizes the geometric behavior of intermediate layers in residual networks and proposes a new conjecture—”asymptotic forward collapse”—which states that the degree of feature collapse in deep neural networks increases layer by layer during forward propagation. Based on the property that residual networks approximate geodesics in Wasserstein space at the end of training under weight decay, we derive an easily analytical model and verify through experiments on multiple datasets that the PFC metric does indeed monotonically decrease with network depth. This study extends the neural collapse phenomenon to asymptotic forward collapse, thus establishing a theoretical framework for the collapse behavior of intermediate layers and its dependence on input data, providing a new theoretical foundation for understanding the representation learning mechanism of residual networks in classification problems.

The team inaugurates an interdisciplinary research paradigm. Its flagship contribution is “functional game-graph theory,” a synthesis of functional mapping, evolutionary game theory, and graph theory that furnishes a formal framework for dissecting the genetic-regulatory networks underlying complex biological traits (Hortic. Res. 2025). Deployed across oncology, pharmacology, and planetary science, the framework elucidates tumor-microenvironment interactions (Phys. Life Rev. 2025), forecasts drug-response profiles (Drug Discov. Today 2025), and extracts patterns from planetary datasets (Nat. Commun. 2024).

Research Outputs

1. Fa, C., Wang, G., Pan, W., Wang, Y., Che, J., Dong, A., Yang, D., Wu, R., Yau, S.-T. & Sun, L. (2025). An omnigenic interactome model to chart the genetic architecture of individual plants. Horticulture Research, uhaf345.
   By integrating the Functional Mapping methodology pioneered by Professor Rongling Wu with the idopNetwork framework developed by his team after joining BIMSA, this work fundamentally transforms the ability of GWAS to resolve the genetic architecture of complex traits. Within this framework, Functional Mapping serves as the core computational engine, precisely capturing the continuous dynamic trajectories of plant growth and development and estimating the dynamic genetic effect values of each genotype at every genetic locus. These estimates provide critical data support for idopNetworks to construct complex, dynamic gene–gene interaction networks at the individual level. This represents a landmark and highly significant achievement.
2. Wang, Y., & Wu, R. (2025). Network stress: A wiring diagram of whole stress genes. Horticulture Research, uhaf302.
   This study proposes a novel theoretical framework—Functional Game-Graph Theory (FunGG)—designed to systematically delineate the genetic control mechanisms of stress responses using conventional mapping or association populations. FunGG integrates Functional Mapping, Evolutionary Game Theory, and Graph Theory, treating stress responses as dynamic processes jointly regulated by multiple genes and constructing comprehensive “circuit diagrams” that encompass all genes and their interactions.
3. Che, J., Wang, Y., Feng, L., Gragnoli, C., Griffin, C., & Wu, R. (2025). High-order interaction modeling of tumor-microenvironment crosstalk for tumor growth. Physics of Life Reviews, 54, 11-23.
   This study couples evolutionary game theory with niche theory and allometric growth theory to establish a higher-order interaction network strategy for decoding tumor–microenvironment (TME) crosstalk. We introduce the concepts of “late-mover hypernetworks” and “synchronous-mover hypernetworks”, in which tumor size and the independent components of gene expression from both tumors and the TME are encoded as nodes, pairwise interactions as edges, and higher-order interactions as hyperedges. This framework enables, for the first time, the quantitative characterization of causal higher-order interactions among tumors, the TME, and tumor size. Our results reveal that genes can promote or suppress tumor growth by modulating “cooperation–competition”dynamics, thereby reversing tumor progression. By overcoming the inability of traditional ligand–receptor frameworks to quantify interaction strength and causality, this approach provides rigorous scientific guidance for the identification of novel targets for precision intervention.
4. Wang, Y., Zhao, J., He, X., Yang, D., Jin, Y., & Wu, R. (2026). A Computational Ecological Genetic Model of Phenotypic Plasticity in Species Interactions. Molecular Ecology Resources, 26(1), e70095.
   Phenotypic plasticity is a fundamental biological phenomenon, yet its genetic regulatory mechanisms have remained largely unknown. This study presents, for the first time, a computational ecological genetics model that elucidates how gene–gene interactions among species operate within ecological communities, providing an important analytical tool for investigating species evolution and speciation.This represents a landmark and highly significant achievement.
5. D. Y, S. Li, J. Li, X. Tao, Y, Li, C. You (co-corresponding), Zhou X. Enhancing mortality prediction in intensive care units: improving APACHE II, SOFA, and SAPS II scoring systems using long short-term memory, Internal Emerging Medicine (2025)
   This study enhances the traditional APACHE II, SOFA, and SAPS II prognostic scoring systems to dynamically analyze ICU patients’ time-series data.
6. Z. Xu, W. Duan, S. Yuan, X. Zhang, C. You, J.-T. Yu, J. Wang, J.-D. Li, S. Y. Shu, Deng, Deep brain stimulation alleviates Parkinsonian motor deficits through desynchronizing GABA release in mice. Nature Communication (2025).
   This study reveals a novel mechanism of deep brain stimulation (DBS) in treating Parkinson’s disease from the perspective of neurotransmitter release dynamics, providing a theoretical basis for optimizing DBS therapeutic strategies and developing more precise neuromodulation approaches.
7. Li, B., Lin, R., Ni, T., G, Yan., M, Burns., J, Li., & Z, Yao. CellScope: high-performance cell atlas workflow with tree-structured representation. Nature Communications (2025).
   The key features of CellScope include multi-level tree-structured visualization, multi-resolution cell type identification, and dynamic gene identity profiling. The framework is built upon our prior work on the manifold fitting theoretical framework. By leveraging manifold fitting, CellScope is able to faithfully recover true cellular signals underlying large-scale gene expression data. The introduction of CellScope provides the single-cell research community with a new solution that is theoretically well grounded, high-performing, and easy to use.
8. Sun, Z., Ye, J., Sun, W., Jiang, L., Shan, B., Zhang, M., Wu，R. & Yuan, J. (2025). Cooperation of TRADD-and RIPK1-dependent cell death pathways in maintaining intestinal homeostasis. Nature Communications, 16(1), 1890.
   Using a novel model, we found that the cooperation between two key genes involved in the apoptotic signaling pathway can significantly maintain the ecological balance of the gut microbiota.
9. Che, J., Jin, Y., Gragnoli, C., Yau, S.T., & Wu, R. (2025). IdopNetwork as a genomic predictor of drug response. Drug Discovery Today, 104252.
   This study proposes a genomic network model, IdopNetwork, for predicting individual drug responses. The proposed approach overcomes the limitations of traditional single-gene or static association analyses by constructing an information-driven, dynamic, and individualized genome-wide interaction network. This framework systematically characterizes the roles of information flow among genes, proteins, and cells in the development of drug efficacy and toxicity. The results demonstrate that IdopNetwork can identify key informational pathways regulating drug responses, thereby providing a new statistical theoretical framework and methodological foundation for precision medicine, drug dosage optimization, and the discovery of novel therapeutic targets.
10. Gao, J., Li, S., Mittelholz, A., Rong, Z., Persson, M., Shi, Z., Klinger, L., Cui, J., Wei, Y., & Pan, Y. (2024). Two distinct current systems in the ionosphere of Mars. Nature Communications, 15, 9704.
    This study, based on MAVEN observations and systematic data analysis, quantitatively reveals for the first time on a global scale two distinct current systems in the Martian ionosphere driven respectively by the solar wind and neutral atmospheric winds, highlighting the critical role of advanced quantitative modeling and data fitting in understanding ionospheric dynamics and energy transport on planets without intrinsic magnetic fields.
11. Shi, Z., Rong, Z. J., Fatemi, S., Dong, C. F., Klinger, L., Gao, J. W., Slavin, J. A., He, F., Wei, Y., Holmström, M., & Barabash, S. (2025). Mercury’s field-aligned currents: Perspectives from hybrid simulations. Journal of Geophysical Research: Planets, 130, e2024JE008610.
    Through three-dimensional hybrid kinetic simulations and rigorous numerical analysis, this work systematically elucidates the generation mechanisms and closure pathways of field-aligned currents at Mercury in the absence of an ionosphere, demonstrating the central role of mathematical modeling in linking planetary interior structure with magnetospheric current systems.
12. Rong, Z. J., Wei, Y., He, F., Klinger, L., Yang, Y. Y., Gao, J. W., Shi, Z., Wang, H. P., Cai, S. H., Qin, H. F., & Zhu, R. X. (2025). The fitting of a dipolar magnetic field.
    This study proposes a novel inversion algorithm that successively separates and stably recovers dipole parameters, overcoming the limitations of traditional multi-parameter fitting methods prone to local optima, and demonstrating the importance of inversion techniques in accurately diagnosing global planetary magnetic fields and localized magnetic anomaly sources.

This team made important progress in the mathematical theory of quantum error correction by finding a general framework for non-concatenated multimode codes. This gives a new route to fault-tolerance for superconducting qubit platforms (Phys. Rev. X 2025). Also, we obtained important results regarding the interplay between the mechanical and radiation pressure in an optomechanical cavity, giving precise analytic results (Phys. Rev. A 2025).

Research Outputs

1. Yijia Xu, Yixu Wang, Christophe Vuillot, and Victor V. Albert, Letting the Tiger out of Its Cage: Bosonic Coding without Concatenation, Phys. Rev. X 15, 041025
   This work utilizes the homological group structures on integers to construct a theoretical framework for multimode non-concatenated quantum error correction codes. Many known code examples can be described using our framework. This work systematically studies error correction properties such as code distance and their relations with the corresponding defining matrices. In this work, we also construct some scalable families of codes, whose error correction properties enhance as the number of modes increases. This work may illuminate the research in many-body physics based on oscillator modes.
2. C. Wang, Spectral property of magnetic quantum walk on hypercube, J. Math. Phys. 66 (2025), 013501.
   This article employs the quantum Bernoulli functional method to establish a magnetic quantum walk model on the hypercube, and rigorously proves that both its spectrum and asymptotic spectrum are stable under magnetic field perturbations, which forms a sharp contrast to previous results.
3. Jorge Russo, Miguel Tierz, Analytical exploration of the optomechanical attractor diagram and of limit cycles, Phys. Rev. A 112, 043522
   We analyze the interplay between mechanical and radiation pressure in an optomechanical cavity system. Our study is based on an analytical evaluation of the infinite Bessel summations involved, which previously had led to a numerical exploration of the so-called attractor diagram. The analytical expressions are then suitable for further asymptotic analysis in opposing regimes of the amplitude, which allows for a characterization of the diagram in terms of elementary functions. Building on this framework, we investigate the emergence and properties of optomechanical limit cycles beyond the constraints of the resolved sideband approximation. By employing a Fokker-Planck formalism originally developed in the context of laser theory and then used in cavity optomechanics, we describe the quantum regime of these limit cycles, offering a more detailed and unified analytical perspective.

The team applies frontier econometric methods and big data analytics to study key economic and social issues. It develops an intelligent framework for detecting financial statement fraud that integrates news coverage with financial disclosures, achieving a recall rate of 98.2% (Management Science, Online). It also provides the first empirical evidence that individuals’ subjective expectations violate additivity over time and shows how such nonadditivity predicts financial investment behavior (Management Science, Online). In addition, the team conducts a systematic evaluation of default-setting effects in the regulation of digital platforms, highlighting their implications for competition policy (American Economic Journal: Microeconomics, 2025).

Research Outputs

1. Jianqing Fan, Qingfu Liu, Bo Wang, and Kaixin Zheng, Unearthing Financial Statement Fraud: Insights from News Coverage Analysis, Management Science, Online.
   This research innovatively develops a comprehensive framework for detecting financial statement fraud by synergistically leveraging news media coverage and textual analysis of financial reports. A key breakthrough is the pioneering use of news reports to capture early signals of undisclosed fraud, combined with the extraction of peer-comparative features from corporate business descriptions. This integrated approach achieves a remarkable recall rate of 98.2% for confirmed fraud cases. The method substantially enhances regulatory monitoring efficiency and offers a novel paradigm for financial risk surveillance.
2. Peter Haan, Chen Sun, Uwe Sunde, Georg Weizsäcker, Nonadditivity of Subjective Expectations over Different Time Intervals, Management Science, Online,
   This study provides the first empirical evidence that individuals’ subjective expectations of economic variables are non-additive over time and demonstrates that this cognitive bias is correlated with one’s financial investment. These findings open a new avenue for research on the formation of subjective beliefs and offer implications for household finance and the measurement of expectations.
3. Francesco Decarolis, Muxin Li, and Filippo Paternollo, Competition and Defaults in Online Search, American Economic Journal: Microeconomics, 17 (3): 369-414 (2025)
   This study presents the first systematic evaluation of policy interventions aimed at weakening the market power of large digital platforms through changes in default settings. Using a comparative empirical analysis of policies implemented in the European Union, Russia, and Turkey, the study demonstrates the significant impact of default options on competition in online search markets and shows that policy effectiveness varies with local market structure, competitor quality, and intervention design. These findings provide new theoretical and empirical foundations for understanding the role of behavioral biases in economic policymaking.
4. Xiaohui Lu and Yahong Zhou, An Adaptive Kernel-Based Structural Change Test for Copulas, Journal of Business & Economic Statistics, 43(3): 696-709 (2025)
   This article proposes a structural change test for copula models based on the kernel smoothing method. The proposed approach enables adaptable estimation of the dynamic marginal distributions, either parametrically or semi-parametrically. Monte Carlo simulations show that the test performs well in finite samples and outperforms existing tests in the case of periodic changes
5. Yufeng Mao and Yayi Yan, An Adaptive Residual-Based Test for Factor Structure, Journal of Business & Economic Statistics, Online,
   This article addresses the critical issue of testing static approximate factor models against unspecified alternatives by proposing an adaptive residual-based test. The methodology is versatile, encompassing alternatives such as factor models with nonlinear factor structures, conditional factor models, and factor models with structural breaks. Simulation studies demonstrate that the test has superior size and power properties.
6. Jun Cai, Jian Zhang, and Yahong Zhou, High-Dimensional Oaxaca-Blinder Decomposition With an Application to Gender and Hukou Discrimination in the Chinese Labour Market, Oxford Bulletin of Economics and Statistics, Online,
   This paper explores the estimation and inference of counterfactual cumulative distribution functions (CDFs) in a high-dimensional setting, with a focus on the distributional Oaxaca–Blinder decomposition. We propose two semi-parametric estimators for the counterfactual CDF, deriving their asymptotic properties and demonstrating that both estimators are semiparametrically efficient, even when using finite-dimensional controls.
7. Zequn Jin, Min Xu, and Yahong Zhou, Non-parametric identification and eStimation of partialeffects with endogeneity and selection, Econometric Reviews, 44(6): 770-801 (2025)
   This study investigates the identification and estimation of heterogeneous partial effects using a non-parametric model. we propose a flexible three-step estimator. The first two steps entail estimating propensity scores to address the endogeneity of the discrete regressor and sample selection issues, whereas the final step employs a pairwise difference estimation strategy to partial out the non-linear term.
8. Xinyu Duan, Qingfu Liu, Zhengyun Xu, Zhiliang Ying, and Xiaohong Zhang, Option Implied Volatility and Trading Strategies Based on Neural Network Correction, Journal of Futures Markets, 46(1): 3-19 (2026)
   This study extends classical option-pricing models by incorporating a neural network correction to capture the intricate nonlinearities of the implied volatility surface. Utilizing SSE 50 ETF option data, we propose a two-stage hybrid framework that first fits a parametric model and subsequently employs a feedforward neural network to correct residual errors, thereby significantly enhancing out-of-sample predictive accuracy across multiple horizons. Empirical validation through a delta-neutral volatility trading strategy demonstrates that this theory-guided machine learning approach outperforms benchmark models in both forecasting and trading performance, yielding superior risk-adjusted returns. Our findings provide novel empirical evidence from the Chinese derivatives market on the practical utility of augmenting financial models with machine learning techniques.
9. Tianxiang Hao, Qingfu Liu, Deyu Miao, and Yiuman Tse, Predicting Commodity Returns Through Image-Based Price Patterns, Journal of Futures Markets, 45(12): 2434-56 (2025)
   This study applies convolutional neural networks (CNNs) to extract predictive signals directly from open-high-low-close (OHLC) price charts of U.S. commodity futures. The empirical results demonstrate that such image-based representations enhance short- and medium-term return predictability and capture nonlinear dependencies beyond traditional financial factors. However, transfer learning from the U.S. to the Chinese market proves ineffective, underscoring that pattern recognition based on visual data requires market-specific adaptation. These findings offer new empirical evidence for the application of computer vision techniques in financial market analysis.
10. Shihan Li, Si Li, Qingfu Liu, and Xiao Wei, Still Water Runs Deep: Soft Power in Chinese Prefectures and Municipalities, Journal of Asian Economics, 98, 101909 (2025)
    This study constructs a dictionary of soft-power-related terms and employs textual analysis on media news data from Chinese prefectures and municipalities to measure regional soft power. The findings reveal a moderately positive causal effect of soft power on local economic development, operating through channels such as attracting tourists and talents, unifying ideological perspectives, and coordinating sustainable growth. This research provides city-level empirical evidence for the significance of soft power in economic growth, emphasizing the necessity of cultivating soft power resources alongside hard power.
11. Qingfu Liu, Lei Lu, Yiuman Tse, and Chuanjie Wang, Sovereign debt risk, government ESG, and bank stock performance, Journal of Asian Economics, 101, 102079 (2025)
    This study, based on monthly data from 578 listed banks across 22 major economies, investigates the adverse impact of sovereign debt risk on bank stock returns and volatility, and finds that government ESG performance significantly mitigates this negative effect. Using China as a case study and constructing a time-varying factor copula framework, the research further reveals that the cross-border spillover effect of external sovereign debt risk on systemic risk within China’s banking sector has intensified since 2017. These findings offer policymakers a new perspective for risk mitigation.
12. Paul Belleflamme, Muxin Li, and Anaïs Périlleux, Sharing Economy Platforms in the Face of Crises: A Conceptual Framework, Sustainability, 17(14), 6370 (2025)
    This study proposes a conceptual framework for analyzing the impact of crises on the sustainability of sharing-economy platforms. By distinguishing the nature of shocks, the temporal dimension, and two-sided network effects, and drawing on cases such as Airbnb and Uber, the study reveals platforms’ dynamic adaptation mechanisms and strategic responses in the short, medium, and long run. The findings provide both theoretical foundations and practical insights for platform crisis management and policy design.
13. Muxin Li, Self-Preferencing in Adjacent Markets, CPI Antitrust Chronicle, Online.
    This study provides an in-depth analysis of digital platforms’ self-preferencing behavior in adjacent markets, systematically examining its underlying incentives and welfare implications. It shows that while such strategies can increase demand for platform-affiliated products, they may also discourage user participation and reduce profits in the core market. The net effect depends on factors such as the strength of network effects, product quality, and the alignment of user preferences. These results offer an important theoretical framework and case-based evidence for understanding platform expansion strategies and for designing targeted antitrust policies.
14. 周亚虹，萧莘玥，金泽群，忻恺，姜帅帅，偏线性分位数选择模型的估计与应用，管理科学学报，2025年第28卷第9期。
    This study investigates the model identification and estimation issues under quantile regression framework for partially linear quantile models in the presence of sample selection. To address selection bias in quantile regression caused by sample selection problems, the research achieves effective correction by modeling the joint distribution of unobserved disturbance terms in both the outcome equation and the selection equation (e.g., using Copula functions).

Research Output

1. Liangliang Shi, Shenhui Zhang, Xingbo Du, Nianzu Yang, Junchi Yan, DSBRouter: End-to-end Global Routing via Diffusion Schrodinger Bridge, Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:55065-55081, 2025.
   This paper proposes the first end-to-end deep global routing solver, DSBRouter, which leverages a Diffusion Schrödinger Bridge (DSB) model for chip routing design. During training, DSBRouter constructs a bridge between the initial pins and the routing results, learning the forward and backward mappings between them. During inference, DSBRouter introduces an evaluation-guided sampling strategy based on routing metrics (such as overflow) to further enhance routing prediction performance. Experimental results demonstrate that DSBRouter achieves state-of-the-art performance in reducing overflow across multiple datasets, and in some cases is even able to generate routing solutions with zero overflow.
2. Liangliang Shi, Haoran Zhang, Shuheng Shen, Changhua Meng, Weiqiang Wang, Junchi Yan, BiQAP: Neural Bi-level Optimization-based Framework for Solving Quadratic Assignment Problems, SIGKDD Conference on Knowledge Discovery and Data Mining V.2.  (2025) 2550-2561
   This paper proposes BiQAP, a deep solver for the Quadratic Assignment Problem (QAP) designed from an intrinsic optimization perspective. By viewing the doubly stochastic constraint output of QAP as the solution to an entropy-regularized Gromov–Wasserstein problem, BiQAP incorporates an alternating iterative Sinkhorn algorithm as a network layer, thereby enhancing both representational capacity and constraint satisfaction. Experimental results show that on Koopmans–Beckmann–type QAP datasets, BiQAP significantly outperforms heuristic methods, matrix-iteration approaches, and other neural network–based methods.
3. Wenzhi Gao, Ya-Chi Chu, Yinyu Ye, Madeleine Udell, Gradient Methods with Online Scaling, Proceedings of Thirty Eighth Conference on Learning Theory, PMLR 291:2192-2226, 2025.
   This paper proposes a framework for accelerating the convergence of gradient-based methods in online learning. Unlike traditional worst-case analyses, the framework provides strong convergence guarantees for optimal step sizes tailored to the actual iteration trajectories, and yields improved complexity results for smooth and strongly convex optimization. For smooth convex optimization, the framework also establishes, for the first time, convergence guarantees for the widely used hypergradient descent heuristic.
4. Junyi Zhang, Yiming Wang, Yunhong Lu, Qichao Wang, Wenzhe Qian, Xiaoyin Xu, David Gu, Min Zhang, Spherical Geometry Diffusion: Generating High-quality 3D Face Geometry via Sphere-anchored Representations, AAAI Conference on Artificial Intelligence. (2026)
   This paper proposes a novel framework called Spherical Geometry Diffusion, which aims to generate high-quality 3D face geometry using spherical manifold representations. To address the core challenges in existing 3D face generation methods, such as the difficulty in establishing clear topological connections and poor geometric quality, the paper introduces Spherical Geometry Representation (SGR). By anchoring 3D facial geometry signals onto a uniform spherical coordinate system and unfolding them into a unified 2D image, SGR effectively solves the grid connectivity problem and seamlessly integrates with mature 2D generation models. Building upon this, the paper introduces a conditional diffusion model that jointly models geometry and texture, enabling explicit geometric guidance for texture synthesis, achieving diverse and controllable generation. Experiments show that the method outperforms existing approaches in terms of geometric quality, fidelity, and inference efficiency for tasks such as text-based 3D generation, face reconstruction, and editing.
5. Tongliang Zhang, Haibin Kan, Lijing Zheng, Jie Peng, Hanbing Zhao: Further results on permutation pentanomials over finite fields with characteristic two. Des. Codes Cryptogr. 93(9): 4083-4112 (2025)
   This paper investigates the permutation cryptographic properties of several classes of pentanomials f(x) over finite fields with characteristic two. By introducing a new concept of irreducible polynomials—zero-trace polynomials—the authors identify sufficient conditions for f to be a permutation polynomial. This resolves a previously open problem. Numerical simulations show that the identified sufficient conditions are also necessary.
6. Chenmiao Shi, Jie Peng, Haibin Kan, Jinjie Gao: On CCZ-equivalence of two new APN functions in trivariate form. Des. Codes Cryptogr. 93(10): 4595-4625 (2025)
   Determining the CCZ-equivalence among infinite classes of existing APN (Almost Perfect Nonlinear) functions is one of the key issues in cryptographic functions. Gologlu et al. obtained results on the non-equivalence of bijective APN functions. The authors naturally extend the study to trivariate cases. Recently, Li Kangquan et al. constructed two classes of infinite trivariate APN function classes, and this paper proves that these two classes are EL-equivalent, also determining the number of non-equivalent functions contained within these two classes. This is the first study on the CCZ-equivalence of APN functions in trivariate representations.
7. Dongliang Cai, Borui Chen, Liang Zhang, Kexin Li, Haibin Kan: Blockchain-enabled reliable outsourced decryption CP-ABE using responsive zkSNARK for mobile computing. Future Gener. Comput. Syst. 176: 108182 (2026)
   Ciphertext-policy attribute-based encryption (CP-ABE) is a promising access control scheme for mobile computing, but its heavy decryption overhead limits widespread application. A common approach is to outsource decryption to cloud servers (DCS); however, existing solutions lack mechanisms to protect honest DCS from false accusations. To address this, the paper proposes a blockchain-based reliable outsourced decryption framework that balances verifiability and exemption without increasing ciphertext redundancy. By combining efficient zkSNARK-based on-chain verification with a challenge-response mechanism, the framework effectively reduces the cost of proof generation and uses blockchain to ensure fair incentives and decentralized outsourcing. Experiments show that under the same decryption cost, the proposed scheme’s Gas consumption on Ethereum is significantly lower than that of Ge et al.’s (TDSC’24) solution (with a maximum reduction of 140 times). Finally, the framework’s application in electric vehicle data sharing scenarios demonstrates its potential to further expand mobile computing resource utilization.