##### Professor

Email: lianbong _at_ simis.cn

Research Fields: Representation Theory, Calabi-Yau Geometry, and String theory.

Office No.:

## Bio

Bong Lian, Vice President of Shanghai Institute of Mathematics and Interdisciplinary Sciences (SIMIS). Before joining SIMIS, he has been a professor at Brandeis University in Boston, Massachusetts. In 1991, he received his PhD in physics from Yale University. He was a postdoctoral fellow at the University of Toronto, Yale University, and Harvard University. He joined the Mathematics Department at Brandeis in 1995 and has remained there since. Professor Lian’s research is at the intersection of mathematics and physics, and he is interested in questions about deformations of Calabi-Yau manifolds. His research interests also include representation theory and string theory.

## Education Experience

- 1991.05
**Yale University**Physics**PhD** - 1985.06
**University of Toronto**Mathematics and Physics**Bachelor**

## Work Experience

- 2024-
**Shanghai Institute for Mathematics and Interdisciplinary Sciences**Vice President - 1995-
**Brandeis University**Professor - 2004-2007
**National University of Singapore**Professor - 1991-1995
**University of Toronto, Yale University, Harvard University**Postdoctoral Fellow

## Honors and Awards

- A.P. Sloan Graduate Dissertation Fellowship in Mathematics (’90–’91)
- Vice President of the International Science Foundation of Cambridge (’16–)
- John Simon Guggenheim Fellowship (’03)
- Scientific committee member of AMC2005 (Singapore ’05)
- Editorial board member of Asian Journal of Mathematics (’07–)
- Chern Prize (’13)
- ICCM Treasurer (’13–)
- Director, Yau Tsinghua Mathcamp (’14–)
- Director, Yau High School Science Awards, U.S.A. Division (’18–)
- ICCM Best Paper Award ’18
- ICCM Best Paper Award ’19
- Editorial board member of Pure and Applied Mathematics Quarterly (’18–)

## Students

## Publications

- (with T.J. Lee, M. Romo, and L. Santilli) GLSM for complete intersections, and mirror symmetry, preprint 2023.
- (with T.J. Lee and M. Romo) Non-commutative resolutions as mirrors of singular Calabi-Yau varieties, preprint 2023.
- (with T.J. Lee and S.-T. Yau) Fractional complete intersections, to appear in American Journ. Math. 2024.
- (with A. Linshaw), Vertex algebras and commutative algebras, Harvard CMSA MathScience Literature Lecture Series 2022.
- (with Y. Kim and T.J. Lee), Mirror symmetry for partial flag varieties of type C, preprint 2021.
- (with D. Zhang and T.J. Lee), On a conjecture of Huang-Lian-Yau-Yu, submitted to Comm. Anal. and Geom.
- (with S. Hosono, T.J. Lee, S.-T. Yau), Mirror symmetry for double cover Calabi–Yau varieties, submitted to JDG; arXiv:2003.07148.
- (with S. Hosono, H. Takagi, S.-T. Yau), K3 surfaces from configuations of six lines in P 2 and mirror symmetry II – λK3-functions, arXiv:1903.09373. To appear in Int. Math. Res. Notices.
- (with S. Hosono, H. Takagi, S.-T. Yau), K3 surfaces from configuations of six lines in P 2 and mirror symmetry I, arXiv:1810.00606. To appear in Comm. Num. and Phys.
- (with A. Huang, S.-T. Yau, C.-L. Yu), Jacobian rings for homogenous vector bundles and applications, arXiv:1801.08261 [math.AG]. To appear in Math. Res. Lett.
- (with A. Huang, S.-T. Yau, C.-L. Yu), Period integrals of local complete intersections and tautological systems, arXiv:1801.01194 [math.AG]. To appear in Math. Res. Lett.
- (with A. Huang, S.-T. Yau, C.-L. Yu), Hasse-Witt matrices, unit roots and period integrals, arXiv:1801.01189 [math.AG, math.NT]. To appear in Math. Ann.
- (with A. Huang, S.-T. Yau, C.-L. Yu), Period integrals and tautological systems, Surveys in Diff. Geom., Vol. 22, No. 1 (2018), pp. 275-289.
- (with J. Chen, A. Huang and S.-T. Yau), Differential Zeros of Certain Special Functions, Comm. Num. Th. Phys. Vol. 12, No. 4 (2018), pp. 609-655. arXiv:1709.00713 [math.AG].
- (with M. Zhu), On the hyperplane conjecture for periods of Calabi-Yau hypersurfaces in P n , Journ. Diff. Geom. Vol. 104, No. 2 (2017), 325-369. arXiv:1610.07125v1.
- (with A. Huang, S.T. Yau, and X. Zhu), Chain integral solutions to tautological systems, arXiv:1508.00406, Math. Res. Lett. Volume 23, Number 6, 1721-1736, 2016.
- (with J. Chen), Calabi-Yau Bundles over Compact K¨ahler Manifolds, submitted, arXiv:1411.2332.
- (with J. Chen and A. Huang), Holonomic Systems for Period Mappings, Nucl. Phys. B, Vol. 898 (2015), pp. 693-706.
- (with A. Huang and X. Zhu), Period Integrals and the Riemann-Hilbert Correspondence, J. Diff. Geom. Vol. 104, No. 2 (2016), pp. 325-369. arXiv:1303.2560v1.
- (with S. Bloch, A. Huang, V. Srinivas and S.-T. Yau), On the Holonomic Rank Problem, J. Diff. Geom. 97 (2014), 11–35. arXiv:1302.4481v1.
- (with R. Song and S.-T. Yau), Period Integrals and Tautological Systems, Journ. EMS Vol. 15, 4 (2013) 1457-1483.
- (with S.-T. Yau), Period Integrals of CY and General Type Complete Intersections, Invent. Math. Vol. 191, 1 (2013) 35-89.
- (with S. Li and S.-T. Yau), Picard-Fuchs Equations for Relative Periods and AbelJacobi Map for Calabi-Yau Hypersurfaces, Amer. J. Math. Vol. 134, No. 5 (2012) 1345-1384. arXiv:0910.4215 [math.AG]
- (with A. Linshaw and B. Song), Chiral Equivariant Cohomology of Spheres, Contemp. Math. vol. 557 (2011), 41-75.
- (with A. Linshaw and B. Song), Chiral Equivariant Cohomology III, Amer. J. Math. 132, No. 6 (2010), 1549-1590.
- (with J. Wiczer), Genus Zero Modular Functions, arXiv:math/0611291.
- (with B. Song), A Convexity Theorem and Reduced Delzant Spaces, Advanced Lectures in Mathematics, Vol. 13 (2010), 61-96.
- (with K. Liu), Localization and Some Recent Applications, Advanced Lectures in Mathematics, Vol. 13 (2010), 97-138.
- (with A. Linshaw), Howe Pair and Vertex Algebras, J. Algebra 317 (2007), 111-152.
- (with A. Linshaw and B. Song), Chiral Equivariant Cohomology II, Trans. Am. Math. Soc. 360 (2008), 4739-4776.
- (with B. Song), Reduced Delzant Spaces and a Convexity Theorem, Topology, Vol. 46, No. 6, (2007), 554-576.
- (with A. Linshaw), Chiral Equivariant Cohomology I, Advances in Math. 209 (2007) 99-161.
- An Introduction to Chiral Equivariant Cohomology, proceedings of the International Congress of Chinese Mathematicians, Hong Kong 2005.
- (with S. Hosono, K. Oguiso and S.T. Yau), Counting Unimodular Lattices in Rr,s , preprint.
- (with A. Todorov and S.-T. Yau), Maximal Unipotent Monodromy for Complete Intersection CY Manifolds, Amer. J. Math. 127 (2005), no. 1, 1–50.
- (with S. Hosono, K. Oguiso and S.T. Yau), Autoequivalences of Derived Category of A K3 Surface and Monodromy Transformations, J. Algebraic Geom. 13 (2004), no. 3, 513–545.
- (with S. Hosono, K. Oguiso and S.T. Yau), Counting Fourier-Mukai Partners and Applications, in Algebraic structures and moduli spaces, 177–192, CRM Proc. Lecture Notes, 38, Amer. Math. Soc., Providence, RI, 2004.
- (with S. Hosono, K. Oguiso and S.T. Yau), Fourier-Mukai Partners of a K3 surface of Picard number one, in Vector Bundles and Representation Theory, 43–55, Contemp. Math. 322, Amer. Math. Soc., Providence, RI, 2003.
- (with S. Hosono, K. Oguiso and S.T. Yau), c=2 Rational Conformal Field Theories via the Gauss Product, hep-th/0211230, Comm. Math. Phys. 241 (2003) 245-286.
- (with S. Hosono, K. Oguiso and S.T. Yau), Kummer structures on a K3 surface – An old question of T. Shioda, math.AG/0202082, Duke Math. Journ. Vol. 120. No. 3 (2003) 635-647.
- (with C.H. Liu, K. Liu and S.T. Yau), S 1 -fixed points of Quot Schemes and Mirror Principle computations, math.AG/0111256, Contemp. Math. vol. 322 (2003) 165-194.
- (with K. Liu and S.T. Yau), Towards a Mirror Principle of Higher Genus, Conference Proceedings on Geometry and Physics August 2001, Zhejiang Univ, Hangzhou. AMS/IP Studies in Adv. Math. vol. 29 (2002) 77-86.
- (with K. Liu and S.T. Yau), Some Applications of Mirror Principle, Conference Proceedings SISTAG July 2001, Contemp. Math. vol. 314 (2002) 161-167.
- (with S.T. Yau), The nth Root of the Mirror Map, Conference Proceedings on Arithmetic and Physics of Calabi-Yau Varieties, Fields Inst. Aug 2001, Fields Inst. Comm. Vol. 38 (2003) 195-199.
- (with C.H. Liu and S.-T. Yau), A Reconstruction of Euler Data, Journ. Alg. Geom. 12 (2003) 269-284.
- (with K. Liu and S.-T. Yau), Mirror Principle IV, Surveys Diff. Geom. vol. 7 (2001) 475-496.
- (with K. Liu and S.-T. Yau), A Survey of Mirror Principle, AMS/IP Studies in Adv. Math. Vol. 33 (2002) 3-10.
- (with K. Liu and S.-T. Yau), Mirror Principle III, Asian J. Math. 3 (2000), no. 4, 771-800.
- (with S.-T. Yau), A Tour of Mirror Symmetry, First International Congress of Chinese Mathematicians (Beijing, 1998), 115–127, AMS/IP Stud. Adv. Math., 20, Amer. Math. Soc., Providence, RI, 2001.
- (with S.-T. Yau), Differential Equations from Mirror Symmetry, Surveys Diff. Geom. Vol. 5 (1999) 510-526.
- Lectures on Mirror Symmetry, School on Differential Geometry at ICTP, Trieste 1999.
- (with K. Liu and S.-T. Yau), Mirror Principle, A Survey, Current Developments in Mathematics 1998 (Cambridge, MA), 35-82, Int. Press, Somerville, MA, 1999.
- (with K. Liu and S.-T. Yau), Mirror Principle II, Asian J. Math. Vol. 3, No. 1 (1999) 109-146.
- (with K. Liu and S.-T. Yau), The Candelas-de la Ossa-Green-Parkes Formula, Nucl. Phys. B67 (1999) 106-114.
- (with K. Liu and S.-T. Yau), Mirror Principle I, Asian J. Math. Vol. 1, No. 4 (1997) 729-763.
- (with A. Klemm, S.S. Roan and S.-T. Yau), Calabi-Yau fourfolds for M- and F-theory compactifications, hep-th/9701023, Nucl. Phys. B518 (1999) 515-574.
- (with S. Hosono and S.-T. Yau), Maximal degeneracy points of GKZ systems, alggeom/9603014, JAMS Vol. 10, No. 2 (1997) 427-443.
- (with S. Hosono and S.-T. Yau), Calabi-Yau varieties and pencils of K3 surfaces, alggeom/9603020.
- (with S. Hosono) GKZ hypergeometric systems and applications to mirror symmetry, Frontiers in quantum field theory (Osaka, 1995), 86–95, World Sci. Publishing, River Edge, NJ, 1996.
- (with S. Hosono and S.-T. Yau), GKZ-Generalized Hypergeometric Systems in Mirror Symmetry of Calabi-Yau Hypersurfaces, alg-geom/9511001, Commun. Math. Phys. 182 (1996) 535-578.
- (with S.-T. Yau), Arithmetic properties of mirror maps and quantum couplings, Commun. Math. Phys. 176, no. 1 (1996).
- (with S.-T. Yau), Integrality of Certain Exponential Series, (Mirror maps, modular relations and hypergeometric series I), hep-th/9507151, Algebra and geometry (Taipei, 1995), 215–227, Lect. Algebra Geom., 2, Internat. Press, Cambridge, MA, 1998.
- (with S.-T. Yau), Mirror maps, modular relations and hypergeometric series II, in Proceedings of the Conference on S-duality in Triste ICTP 1995, Nucl. Phys. B46 (1996) 248-262, hepth-th/9507153.
- (with G.J. Zuckerman), From String Backgrounds to Topological Field Theories, RIMS Proceedings of Symposium on BRS Symmetry 1995, hep-th/9512039.
- (with G.J. Zuckerman), Algebraic and Geometric Structures in String Backgrounds, hep-th/9506210, Strings ’95 (Los Angeles, CA, 1995), 323–335, World Sci. Publishing, River Edge, NJ, 1996.
- (with G.J. Zuckerman), Commutative quantum operator algebras, Jour. Pure Appl. Alg. 100 (1995) 117-139, q-alg/9501014.
- (with G.J. Zuckerman), Moonshine cohomology, RIMS proceedings on Vertex Operator Algebras and the Monster 1995, q-alg/9501025.
- (with S.-T. Yau), Mirror symmetry, rational curves on algebraic manifolds and hypergeometric series, XIth International Congress of Mathematical Physics (Paris, 1994), 163–184, Internat. Press, Cambridge, MA, 1995.
- (with A. Klemm, S.-S. Roan and S.-T. Yau), A note on ODEs from mirror symmetry, Functional analysis on the eve of the 21st century, Vol. II (New Brunswick, NJ, 1993), 301–323, Progr. Math., 132, Birkhuser Boston, Boston, MA, 1996.
- (with G.J. Zuckerman), Some classical and quantum algebras, Prog. Math. Vol 123 (1994) 509-529, hep-th/9404010.
- (with G.J. Zuckerman), New perspectives on the BRST-algebraic structure of string theory, Comm. Math. Phys. 154 (1993) 613, hep-th/9211072.
- On the classification of simple vertex operator algebras, Commun. Math. Phys. 163 (1994) 307.
- (with G.J. Zuckerman), Semi-infinite homology and 2D gravity (I), Commun. Math. Phys. 145 (1992) 561.
- (with G.J. Zuckerman), 2d gravity with c=1 matter, Phys. Lett. B266 (1991) 21.
- (with G.J. Zuckerman), New selection rules and physical states in 2d gravity; conformal gauge, Phys. Lett B254, No.3,4 (1991) 417.
- (with G.J. Zuckerman), An application of infinite-dimensional Lie theory to semisimple Lie groups, Contemp. Math. 145 (1993) 249-257.
- (with G.J. Zuckerman), BRST cohomology and non-compact coset models, Proceedings of the XXth International Conference on Differential Geometric Methods in Theoretical Physics, Vol. 1, 2 (New York, 1991), 849–865, World Sci. Publishing, River Edge, NJ, 1992.
- (with G.J. Zuckerman), BRST cohomology and highest weight vectors I, Commun. Math. Phys. 135 (1991) 547.
- (with G.J. Zuckerman), BRST cohomology of the super-Virasoro algebras, Commun. Math. Phys. 125 (1989) 301.
- (with C.A. Lin), Chaotic behavior in a low-order unforced, inviscid barotropic model, PAGEOPH 124, No.6 (1986).