# Bong Lian

Degrees

Yale University, Ph.D.University of Toronto, B.A.

Expertise

Representation theory. Calabi-Yau geometry. String theory.Profile

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My research lies at the interface between algebra, geometry, and physics. I study the interplay between representations theory, Calabi-Yau geometry and string theory. Intuitions and insights from one theory can often manifest themselves in a powerful and sometimes surprising ways to help solve problems in another theory. Webpage

Courses Taught

MATH | 22a | Honors Linear Algebra and Multi-variable Calculus, Part I |

MATH | 100a | Introduction to Algebra, Part I |

MATH | 140a | Geometry of Manifolds |

Awards and Honors

2018 ICCM Best Paper Gold Award, for joint paper with S.-T. Yau (2018 - 2019)

2017 ICCM Best Paper Ruok-Lin Award for my joint paper with S.-T. Yau (2017)

2017 ICCM Best Paper Silver Award, for my joint paper with A. Huang and X. Zhu (2017)

Chern Prize (ICCM 2013 Taipei) (2013 - 2006)

Plenary speaker at the 2013 International Congress of Chinese Mathematicians (Taipei) (2013)

President of International Science Foundation of Cambridge (2009)

Guggenheim Fellowship (2004 - 2003)

Sloan Graduate Dissertation Fellowship (1990)

Scientific committee member Asian Mathematics Congress 2005 (1989 - 1990)

Secretary of the Int'l Science Foundation of Cambridge (1988 - 1989)

Scientific committee member of Intl. Congr. of Chinese Mathematicians (1983)

Scholarship

B. Lian and A. Linshaw). "Vertex algebras and commutative algebras." __preprint 2021__ (2021)

T.J. Lee, B. Lian and S.-T. Yau. "Fractional Complete Intersections." __preprint 2021__ (2021)

Y. Kim, T.J. Lee and B. Lian. "Mirror symmetry for partial flag varieties of type C." __Preprint 2021.__ (2021)

A. Huang, B.H. Lian, S.-T. Yau and C.-L. Yu. "Hasse-Witt matrices, unit roots and period integrals." __arXiv:1801.01189 [math.AG, math.NT] Submitted to Ann. Math.__ (2020)

A. Huang, B.H. Lian, S.-T. Yau and C.-L. Yu. "Jacobian rings for homogenous vector bundles and applications." __arXiv:1801.08261 [math.AG]. Accepted for publication by Comm. Num. and Phys. 2020.__ (2020)

A. Huang, B.H. Lian, S.-T. Yau and C.-L. Yu. "Period integrals of local complete intersections and tautological systems." __arXiv:1801.01194 [math.AG]. Accepted for publication in Math. Res. Lett.__ (2020)

S. Hosono, B. Lian, H. Takagi, S.-T. Yau. "K3 surfaces from configuations of six lines in P^2 and mirror symmetry I." __arXiv:1810.00606. Submitted to Int. Math. Res. Notices 2020.__ (2020)

S. Hosono, B. Lian, H. Takagi, S.-T. Yau. "K3 surfaces from configuations of six lines in P^2 and mirror symmetry II." __arXiv:1903.09373. Accepted for publication in Math. Res. Notices.__ (2020)

S. Hosono, T.J. Lee, B. Lian and S.-T. Yau. "Mirror symmetry for double cover Calabi--Yau varieties II." __Preprint 2020.__ (2020)

S. Hosono, T.J. Lee, B. Lian, S.-T. Yau. "Mirror symmetry for double cover Calabi--Yau varieties I." __arXiv:2003.07148__ (2020)

T.J. Lee, B. Lian and D. Zhang. "On a conjecture of Huang–Lian–Yau–Yu." __Preprint 2020. Submitted to Comm. Analy. and Geom. 2020.__ (2020)

T.J. Lee, B. Lian, A. Sheshmani, S.-T. Yau. "From the Ooguri-Vafa metric to a Calabi-Yau metric." __preprint__ (2019)

T.J. Lee, B. Lian, A. Sheshmani, S.-T. Yau. "GW invariants and Chen-Ruan cohomology of cyclic cover Calabi-Yau varieties." __preprint__ (2019)

A. Huang, B. Lian, C.-L. Yu, S.-T. Yau. "Period integrals and tautological systems." __Surveys in Diff. Geom.__ 22. 1 (2018): 275-289.

B.H. Lian and M. Zhu. "On the hyperplane conjecture for periods of Calabi-Yau hypersurfaces in P^n." __arXiv:1610.07125v1__ (2017)

J. Chen, A. Huang, B.H. Lian, S.-T. Yau. "Differential Zeros of Certain Special Functions." __arXiv:1709.00713__ (2017)

A. Huang, B.H. Lian and X. Zhu. "Period Integrals and the Riemann-Hilbert Correspondence." __J. Diff. Geom.__ 104. 2 (2016): 325-369.

A. Huang, B.H. Lian, S.-T. Yau and X. Zhu. "Chain Integral Solutions to Tautological Systems." __Math. Res. Letters (2016)__ 23. 6 (2016): 1721-1736.

Chen, Jingyue and Lian, Bong. "CY Principle Bundles over Compact Kahler Manifolds." __submitted__ arXiv:1411.2332. (2016).

J. Chen, A. Huang and B.H. Lian. "Holonomic Systems for Period Mappings." __Nucl. Phys. B__ 898. (2015): 693-706..

Bloch, S., Huang, A., Lian, B., Srinivas, V., Yau, S.-T.. "On the Holonomic Rank Problem." __J. Diff. Geom. 97 (2014), 11–35.__ (2014).

Bong Lian, Ruifang Song and Shing-Tung Yau. "Period Integrals and Tautological Systems." __JEMS__ 15. 4 (2013): 1457-1483..

Lian, Bong and Shing-Tung Yau. "Period Integrals of CY and General Type Complete Intersections." __Inventiones Mathematicae__ 191. 1 (2013): 35-89.

Bong Lian, Si Li and Shing-Tung Yau. "Picard-Fuchs Equations for Relative Periods and Abel-Jacobi Map for Calabi-Yau Hypersurfaces." __American Journal of Mathematics__ 134. 5 (2012): 1345-1384.

Bong Lian, Andrew Linshaw, and Bailin Song. "Chiral Equivariant Cohomology of Spheres." __Contemporary Mathematics__ 557. (2011): 41-75.

B. Lian and B. Song. "Convexity and Reduced Delzant Spaces." __Advanced Lectures in Mathematics__ Vol. 13. (2010): 61-96.

Bong Lian and Kefeng Liu. "Localization and Some Recent Applications." __Advanced Lectures in Mathematics__ Vol. 13. (2010): 97-138.

Bong Lian, Andrew Linshaw, and Bailin Song. "Chiral Equivariant Cohomology III." __American Journal of Mathematics__ Vol. 132. No. 6 (2010): 1549-1590.

B. Lian, A. Linshaw and B. Song. "Chiral Equivariant Cohomology II." __Transactions of AMS__ 360 (2008): 4739-4776.

B. Lian and A. Linshaw. "Chiral Equivariant Cohomology I." __Advances in Mathematics__ 209. (2007): 99-161.

B. Lian and B. Song. "Reduced Delzant Spaces and a Convexity Theorem." __Topology__ Vol. 46. No. 6 (2007): 554-576.

B. Lian, A. Todorov and S.-T. Yau. "Maximal Unipotent Monodromy for Complete Intersection." __American Journal of Mathematics__ 127. 1 (2005): 1--50.

B. Lian, S. Hosono, K. Oguiso and S.T. Yau. "Autoequivalences of Derived Category of a K3 Surface and Monodromy Transformations." __Journal of Algebraic Geom.__ 13. 3 (2004): 513--545.

B. Lian, S. Hosono, K. Oguiso and S.T. Yau. "Counting Fourier-Mukai Partners and Applications." __CRM Proc. Lecture Notes__ 38. (2004): 177--192.

B. Lian and S.T. Yau. "The nth Root of the Mirror Map." __Fields Institute Communications__ 38. (2003): 195-199.

B. Lian, S. Hosono, K. Oguiso and S.T. Yau. "c=2 Rational Conformal Field Theories." __Communications in Math. Physics__ 241. (2003): 245-286.

B. Lian, C.H. Liu and S.T. Yau. "A Reconstruction of Euler Data." __Journal of Algebraic Geometry__ 12. (2003): 269-284.

B. Lian, C.H. Liu, and S.T. Yau. "A Reconstruction of Euler Data." __Journal of Algebraic Geometry__ 322. (2003): 165-194.

B. Lian, C.H. Liu, and S.T. Yau. "S^1-fixed points of Quot Schemes and Mirror Principle computations." __Conptemporary Mathematics__ 322. (2003): 165-194.

B. Lian, S. Hosono, K. Oguiso, and S.T. Yau. "Kummer structures on a K3 surface - An old question of T. Shioda." __Duke Math. Journal__ 120. 3 (2003): 635-647.