Leonardo Santilli

个人简介

My research interests revolve around mathematical physics, and especially string theory. I study supersymmetric field theories and their relations with algebraic and enumerative geometry, using superstring and M-theory as an overarching framework. I am currently interested in non-commutative Calabi-Yau resolutions, as well as the connection between supersymmetric QFTs with defects on one side, and refined enumerative invariants on the other.

Before my appointment as an Assistant professor at the Shanghai Institute of Mathematics and Interdisciplinary Sciences in August 2025, I was a Shuimu postdoctoral fellow at the Yau Mathematical Sciences Center of Tsinghua University, from 2022 to 2025. I received my PhD in Mathematics in 2022 from the University of Lisbon.

教育经历

• 2018.3-2022.5 University of Lisbon Mathematics PhD
• 2016.9-2017.7 University of Valencia Mathematics Master
• 2015.9-2016.9 University of Valencia Physics Master
• 2012.9-2015.9 La Sapienza University of Rome Physics Bachelor

工作经历

• 2022.10 – 2025.7 YMSC, Tsinghua University Postdoc

荣誉和获奖

• 2023.07 – 2025.07 Tsinghua University Shuimu Scholar
• 2023 Best Doctoral Thesis Award in Mathematical Sciences , FCiencias, Portugal.

论著

[1] L. Santilli, “Large N limits of supersymmetric quantum field theories: A pedagogical overview,” Fortsch. Phys. 2025, e70006 [arXiv:2501.05794].

[2] M. Najjar, L. Santilli and Y. N. Wang, “(-1)-form symmetries from M-theory and SymTFTs,” JHEP 134 (2025), 1 [arXiv:2411.19683].

[3] L. Santilli and R. J. Szabo, “Higher form symmetries and orbifolds of two-dimensional Yang-Mills theory,” Lett. Math. Phys. 115 (2025) no.1, 15 [arXiv:2403.03119]

[4] E. Gesteau and L. Santilli, “Explicit large N von Neumann algebras from matrix models,” Adv. Theor. Math. Phys. 28 (2024) no.7, 2245-2429 [arXiv:2402.10262].

[5] D. Perez-Garcia, L. Santilli and M. Tierz, “Hawking-Page transition on a spin chain,” Phys. Rev. Res. 6 (2024) no.3, 033007 [arXiv:2401.13963].

[6] C. Nunez, L. Santilli and K. Zarembo, “Linear Quivers at Large-N ,” Commun. Math. Phys. 406 (2025) no.1, 6 [arXiv:2311.00024].

[7] L. Santilli and C. F. Uhlemann, “3d defects in 5d: RG flows and defect F-maximization,” JHEP06 (2023), 136 [arXiv:2305.01004].

[8] M. Akhond, A. Legramandi, C. Nunez, L. Santilli and L. Schepers, “Matrix Models and Hologaphy: Mass Deformations of Long Quiver Theories in 5d and 3d,” SciPost Phys. 15 (2023), 086 [arXiv:2211.13240].

[9] M. Akhond, A. Legramandi, C. Nunez, L. Santilli and L. Schepers, “Massive flows in AdS6/CFT5,” Phys. Lett. B 840 (2023), 137899 [arXiv:2211.09824].

[10] D. Perez-Garcia, L. Santilli and M. Tierz, “Dynamical quantum phase transitions from random matrix theory,” Quantum 8 (2024), 1271 [arXiv:2208.01659].

[11] L. Santilli and M. Tierz, “Crystal bases and three-dimensional N= 4 Coulomb branches,” JHEP03 (2022), 073 [arXiv:2111.05206].

[12] L. Santilli and M. Tierz, “Schur expansion of random-matrix reproducing kernels,” J. Phys. A 54, no. 43, 435202 (2021) [arXiv:2106.04168].

[13] L. Santilli, “Phases of five-dimensional supersymmetric gauge theories,” JHEP 07, 088 (2021) [arXiv:2103.14049].

[14] L. Santilli and M. Tierz, “Multiple phases and meromorphic deformations of unitary matrix models,” Nucl. Phys. B 976, 115694 (2022) [arXiv:2102.11305].

[15] L. Santilli and M. Tierz, “Riemannian Gaussian distributions, random matrix ensembles and diffusion kernels,” Nucl. Phys. B 973, 115582 (2021) [arXiv:2011.13680].

[16] L. Santilli, R. J. Szabo and M. Tierz, “TT-deformation of q-Yang-Mills theory,” JHEP 11, 086 (2020) [arXiv:2009.00657].

[17] L. Santilli and M. Tierz, “Exact results and Schur expansions in quiver Chern-Simons-matter theories,” JHEP 10, 022 (2020) [arXiv:2008.00465].

[18] L. Santilli and M. Tierz, “Exact equivalences and phase discrepancies between random matrix ensembles,” J. Stat. Mech. 2008, 083107 (2020) [arXiv:2003.10475].

[19] L. Santilli and R. J. Szabo and M. Tierz, “Five-dimensional cohomological localization and squashed q-deformations of two-dimensional Yang-Mills theory,” JHEP 06, 036 (2020) [arXiv:2003.09411].

[20] L. Santilli and M. Tierz, “SQED3 and SQCD3: Phase transitions and integrability,” Phys. Rev. D 100, no.6, 061702 (2019) [arXiv:1906.09917].

[21] L. Santilli and M. Tierz, “Phase transition in complex-time Loschmidt echo of short and long range spin chain,” J. Stat. Mech. 2006, 063102 (2020) [arXiv:1902.06649].

[22] L. Santilli and M. Tierz, “Large N phase transition in TT -deformed 2d Yang-Mills theory on the sphere,” JHEP 01, 054 (2019) [arXiv:1810.05404].

[23] L. Santilli and M. Tierz, “Phase transitions and Wilson loops in antisymmetric representations in Chern-Simons-matter theory,” J. Phys. A 52, no.38, 385401 (2019) [arXiv:1808.02855].

[24] L. Santilli and M. Tierz, “Complex (super)-matrix models with external sources and q-ensembles of Chern-Simons and ABJ(M) type,” J. Phys. A 53, no.42, 425201 (2020) [arXiv:1805.10543].