I work in the field of mathematical physics and am interested in algebraic and geometric aspects of quantum field theory and string theory.

See Reserach Summary for descriptions of some works listed below.

*On the Hilbert Space of the Chern-Simons Matrix Model, Deformed Double Current Algebra Action, and the Conformal Limit*(with S.Hu, D. Ye, Y. Zhou), arXiv:2409.12486 [math-ph]*Quadratic Duality for Chiral Algebras*(with Z. Gui, K. Zeng)**Adv. Math.**451 (2024) 109791*Topological Quantum Mechanics on Orbifolds and Orbifold Index*(with P. Yang), arXiv:2403.07590 [math.QA]*Quantum Algebra of Chern-Simons Matrix Model and Large N Limit*(with S.Hu, D. Ye, Y. Zhou), arXiv:2308.14046 [math.QA]*Vertex algebras and quantum master equation*.**J.Diff.Geom.**123 (2023), no 3, 461 - 521.*Regularized Integrals on Elliptic Curves and Holomorphic Anomaly Equations*(with J. Zhou).**Commun. Math. Phys.**401, pp 613–645 (2023). <*On the L2-Hodge theory of Landau-Ginzburg models*(with H. Wen).**Adv. Math.**396 (2022) 108165*Landau-Ginzburg mirror symmetry conjecture*(with W. He, Y. Shen, R. Webb).**J. Eur. Math. Soc.**Volume 24, Issue 8, (2022), pp. 2915–2978*Elliptic Trace Map on Chiral Algebras*(with Z. Gui), arXiv:2112.14572 [math.QA]*Regularized Integrals on Riemann Surfaces and Modular Forms*(with J. Zhou).**Commun. Math. Phys.**388, 1403–1474 (2021).*Geometry of Localized Effective Theories, Exact Semi-classical Approximation and the Algebraic Index*(with Z.Gui, K.Xu).**Commun. Math. Phys.**382, 441–483 (2021).*Anomaly cancellation in the topological string*(with K. Costello).**Adv. Theo. Math. Phys.**Vol. 24, No. 7 (2020), pp. 1723-1771.*Dispersionless Integrable Hierarchy via Kodaira-Spencer Gravity*(with W.He, X.Tang, P. Yoo).**Commun. Math. Phys.**379, 327–352 (2020).*Homotopy Algebras in Higher Spin Theory*(with K. Zeng).**Adv. Theo. Math. Phys.**Vol 24, Issue 3, 757-819 (2020)*G-twisted braces and orbifold Landau-Ginzburg Models*(with W. He and Y. Li),**Commun. Math. Phys.**373, no.1, 175–217 (2020).*Calabi-Yau geometry, Primitive form and Mirror symmetry .*,**Adv. Stud. Pure Math.**Primitive Forms and Related Subjects—Kavli IPMU 2014, page 237-268 (2019). Mathematical Society of Japan.*Categorical primitive forms and Gromov-Witten invariants of An singularities*(with A. Caldararu and J. Tu).**Int Math Res Notices,**rnz315 (2019).*Seiberg-Witten differential via primitive forms*(with D. Xie and S.-T. Yau).**Commun. Math. Phys**367, no.1, 193-214 (2019).*Effective Batalin-Vilkovisky Quantization and Geometric Applications*. Proceedings of the 7th ICCM, Vol. I, 349–372,**Adv. Lect. Math.**43.*Unfolding of Orbifold LG B-Models: A Case Study*(with W. He and Y. Li),**PAMQ**14.3 (2018): 443-465.*Some Classical/Quantum Aspects of Calabi-Yau Moduli*.**Trends in Mathematics**, Birkhäuser, Cham. B-Model Gromov-Witten Theory, page 463-497 (2018).*Batalin-Vilkovisky quantization and the algebraic index.*(with R.E.Grady and Q. Li).**Adv. Math.**317 (2017), 575-639.*Mirror symmetry for unimodular exceptional singularities*(with C.Z.Li, K.Saito and Y.Shen).**J. Eur. Math. Soc.**19 (2017), no.4, 1189-1229.*Twisted supergravity and its quantization*(with K. Costello),arXiv:1606.00365[hep-th]*On the B-twisted topological sigma model and Calabi-Yau geometry*(with Q.Li).**J.Diff.Geom.**102 (2016) no.3, 409-484.*Quantization of open-closed BCOV theory, I*(with K. Costello), arXiv:1505.06703[hep-th]*A mirror theorem between Landau-Ginzburg models*.**Nuclear Phys. B.**, 898 (2015).*Primitive forms via polyvector fields*(with C.Z.Li and K.Saito), arXiv:1311.1659[math.AG].*Variation of Hodge structures, Frobenius manifolds, and gauge theory*, arXiv:1303.2782[math.QA].*On the B-twisted quantum geometry of Calabi-Yau manifolds (with Q. Li)*, Proceedings of the Sixth International Congress of Chinese Mathematicians 2013.*Quantum BCOV theory on Calabi-Yau manifolds and the higher genus B-model*(with K.Costello), arXiv:1201.4501[math.QA] .*Renormalization and Mirror symmetry*,**SIGMA Symmetry Integrability Geom. Methods Appl.**8 (2012), 101.*Feynman graph integrals and almost modular forms*,**Comm. in Number Theory and Physics**, 6, 2012.*Picard-Fuchs Equations of Relative Periods and Abel-Jacobi Map for Calabi-Yau Hypersurfaces*(with B.H. Lian and S.-T. Yau),**Amer. J. Math.**134 (2012), no. 5, 1345-1384.*On the spectrum of unitary Finite-Euclidean graphs*(with L.A. Vinh),**Ars Combin.**110 (2013), 275-287.*BCOV theory on the elliptic curve and higher genus mirror symmetry*, arXiv:1112.4063[math.QA].*Morphisms from Azumaya prestable curves with a fundamental module to a projective variety: Topological D-strings as a master object for curves*(with C.H. Liu, R. Song, S.-T. Yau), arXiv:0809.2121[math.AG]*Hamiltonian Formalism of the de-Sitter Invariant Special Relativity*(with M.L. Yan, N.C. Xiao, W. Huang),**Commun. Theor. Phys.**48:27-36, 2007.*Baryonium with a phenomenological skyrmion-type potential*(with M.L. Yan, B. Wu, B. Q. Ma),**Phys.Rev.D**, 72, 2005.**Thesis**:*Calabi-Yau geometry and higher genus mirror symmetry*, Harvard University, 2011

*Effective Batalin-Vilkovisky quantization and geometric applications*, arXiv:1709.00669[math.QA]

----This is an exposition on the effective renormalization of quantum field theory in the Batalin-Vilkovisky formalism. We illustrate its mathematical use by three geometric applications.

Published version at*Proceedings of the 7th ICCM*, Vol. I, 349–372,**Adv. Lect. Math.**43.

*Calabi-Yau geometry, primitive form and mirror symmetry*, available here

----This note explains the connection between K.Saito's theory of primitive forms and B-model Kodaira-Spencer theory on Calabi-Yau geometry.

Published version at**Adv. Stud. Pure Math.**Primitive Forms and Related Subjects—Kavli IPMU 2014, page 237-268 (2019). Mathematical Society of Japan.

*Some classical/quantum aspects of Calabi-Yau moduli.*available here

---- This note explains the basic idea of quantization of Calabi-Yau geometry and higher genus B-model.

Published version at**Trends in Mathematics**, Birkhäuser, Cham. B-Model Gromov-Witten Theory, page 463-497 (2018).*Semi-infinite Hodge structures: from BCOV theory to Seiberg-Witten geometry*, available here

----talk at String-Math 2018.*Introduction to quantization and factorization algebra*, available here

----Lectures at 2021 Higher structures in geometry and physics@ Chern Institute of Mathematics, Nankai University, the 110th anniversary of the birth of Professor Shiing-Shen Chern.

*June 10-14, 2024: 2024 Thematic Program in Field Theory and Topology, Notre Dame, USA**May 17, 2024: Colloquium, 浙江大学数学科学学院.**May 16, 2024: 陈建功大讲堂, 杭州师范大学数学学院.**May 14, 2024: 数智论坛, 南昌大学数学与计算机学院.**May 13, 2024: 数觿讲坛, 南昌航空大学数学与信息科学学院.**May 10, 2024: 珠峰讲坛, 山东大学数学学院.**Apr 25, 2024: 学术讲座, 华中科技大学数学与统计学院.**Apr 24, 2024: 学术讲座, 华中科技大学物理学院.**Apr 23, 2024: 学术讲座, 湖北大学物理学院.**Apr 22, 2024: 学术论坛, 河南大学数学与统计学院.**Apr 3, 2024: Current Developments in Mathematics and Physics, Beijing, China.**Mar 12, 2024: Conference on "Algebraic, analytic, geometric structures emerging from quantum field theory", Chengdu, China.**Feb 28, 2024: 几何讨论班， 四川大学数学系.**Feb 1, 2024: Geometry and Physics Seminar, UC Berkeley, USA.**Jan 24, 2024: Geometry and Physics Seminar, Boston University, USA.**Jan 18, 2024: Algebraic Geometry Seminar, Boston College, USA.**Dec 23, 2023: 学术讲座, 东北师范大学.**Dec 23, 2023: 物理名家讲座, 吉林大学物理系.**Dec 11, 2023: 励新卓越论坛, 首都师范大学数学科学学院.**Dec 4, 2023: 代数几何 讨论班, 南京大学.**Dec 3, 2023: 学术论坛, 南京大学.**Dec 3, 2023: 学术讲座, 东南大学丘成桐中心.**Sep 13, 2023: Eastern Hemisphere Colloquium on Geometry and Physics.**Aug 17, 2023: QM Research Seminar, Center for Quantum Mathematics, Danmark.**July 31, 2023: MIST: Satellite Conference to the ``International Congress of Basic Science", CUHK, Hong Kong.**May 11, 2023: 2023 GADEPs focused conference II: Periods of Calabi-Yau varieties and Gromov-Witten invariants, BIMSA, China.**Apr 27, 2023: 吴文俊实验室讲座, 中国科学技术大学数学系.**Jan 13, 2023: TSIMF 2023 Homological Algebra of the Infrared, Sanya, China.**Nov 2, 2022: The Greater Bay Area Geometry and Mathematical Physics Seminar**Aug 1, 2022: The 9th International Congress of Chinese Mathematicians, Beijing, China.**June 20-24, 2022: Online Workshop on Topology and QFT. University of Notre dame.**Mar 30, 2022: Joint Harvard-CUHK-YMSC Differential Geometry Seminar.**Mar 22-25, 2022: “Geometry, Representation Theory and Quantum Fields”, Osaka City University.**Nov 22–Dec 03 2021: String and M-Theory: The New Geometry of the 21st Century – II, NUS, Singapore.**Nov 22-26, 2021: Higher structures in geometry and physics, Chern Institute of Mathematics, Nankai University**August 2-7, 2021: International Congress on Mathematical Physics (ICMP) 2021 (session Quantum Field Theory), Geneva, Switzerland.**June 14-18, 2021: String-Math 2021 (Plenary talk), IMPA, Rio de Janeiro, Brazil.**May 14, 2021: TQFT Seminar, Instituto Superior Técnico, Lisbon, Portugal.**May 12, 2021: Hodge Seminar, Edinburgh Hodge Institute, Scotland.**May 3, 2021: Online Geometry and Physics Seminar, IASM at Zhejiang University, China.**Dec 27, 2020: ICCM Annual Meeting, USTC, China.**Oct 30, 2020: Wu Wen-ts\"{u}n Lab Lecture, USTC, China.**Sep 20, 2020: ``The 3rd Conference on Operad Theory and Related Topics", Jilin University, China.**Apr 17, 2020: Zoom Mathematical Physics Seminar, Tsinghua University, China.**Dec 11 , 2019: Colloquium, Columbia University, USA.**Dec 9, 2019: Workshop on Symplectic Geometry, NCG and Mathematical Physics, Washington University in St. Louis, USA.**Dec 2, 2019: Geometry, Symmetry and Physics Seminar, Yale, USA.**Nov 25, 2019: Geometry and Topology Seminar, UC Irvine, USA.**Nov 21, 2019: Geometry, Physics and Representation Theory Seminar, Northeastern, USA.**Nov 15, 2019: High Energy Theory Seminar Seminar, IAS, USA.**Nov 8, 2019: Lie Group/Quantum Mathematics Seminar, Rutgers, USA.**Oct 8, 2019: Colloquium, Rutgers- Newark, USA.**June 17-28, 2019: Lectures at summer workshop ``QFT for Mathematicians", Perimeter Institute, Canada.**June 14, 2019: “The mathematical foundations of conformal field theory and related topics” in honor of Yi-Zhi Huang's 60th birthday., Nankai University, Tianjin, China.**June 13, 2019: The 8th International Congress of Chinese Mathematicians (Plenary talk), Beijing, China.**May 6-11, 2019: Deformation theory and homotopy algebras, Emei, China.**Apr 24 and Apr 26, 2019: Mathematical Physics Seminar and GAP Seminar, USTC, China.**Feb 17-24, 2019: BIRS Workshop on Quantum Field Theory and Factorization Algebras, Banff, Canada.**January 25-27, 2019: Workshop on Modular structures in Gromov-Witten theory and related topics , University of Michigan, USA.**Feb 14, 2019: Geometry Seminar, University of Oregon, USA.**Jan 14-18, 2019: Between Topology and Quantum Field Theory in celebration of Dan Freed's 60th birthday, University of Texas at Austin, USA.**Dec 10-14, 2018: Workshop on String and M-theory: the new geometry of the 21 century, IMS at NUS, Singapore.**Nov 24-26, 2018: Mini-Workshop on Hochschild Cohomology and Related Topics III, East China Normal University, China.**Nov 16, 2018: Colloquium at IMS, Shanghaitech University, China.**July 18-22, 2018: String-Math 2018 (Plenary talk), Tohoku University, Japan.**May 10, 2018: 2018 Higher Structures and Symplectic Geometry, Tsinghua University, China.**Feb 8, 2018: Workshop on Factorisation Homology, Factorisation Algebras and the Cobordism Hypothesis, Saint-Etienne de Tinee, France.**Jan 29, 2018: Higher differential geometry seminar, MPIM, Bonn, Germany.**Jan 10-13, 2018: Simons Collaboration Workshop on Homological Mirror Symmetry, Harvard, USA.**Dec 7, 2017: Geometry Seminar, CNU, Beijing.**Nov 16-19, 2017: Gromov-Witten invariants and integrable hierarchies, USTC, China.**Nov 26, 2017: Wu Wen-tsun Lab Lecture, USTC, China.**Oct 30-Nov 4, 2017: East Asia Symplectic Conference 2017, Chengdu, China.**July 31-Aug 11, 2017: Geoquant 2017, Aarhus, Danmark.**July 24-29, 2017: String-Math 2017 (Parallel talk), Hamburg, Germany.**July 20-22, 2017: Flat connections in physics and geometry, Heidelberg, Germany.**July 3-7, 2017: Symposium in Geometry and Differential Equations, Beijing, China.**June 8, 2017: ICTS seminar, USTC, Hefei, China.**May 22-26, 2017: Homological mirror symmetry and higher genus invariants, Simons Center for Geometry and Physics, USA.**May 8-12, 2017: Quantum fields on manifolds with boundary and the BV formalism, Perimeter Institute, Canada.**Apr 28-May 1, 2017: JDG conference on geometry and topology, Harvard, USA.**Apr 25-28, 2017: Developments of mathematics at IPMU: in honor of Kyoji Saito, Kavli IPMU, Japan.**Apr 17-24, 2017: Gauge Equations, Geometry and Strings, ICMAT, Madrid, Spain.**Mar 13-17, 2017: Workshop on homological mirror symmetry, IAS, Princeton, USA.**Feb 6, 2017: Geometry and Physics seminar, IBS-CGP, Korea.**Jan 19, 2017: Ganita seminar, University of Toronto, Canada.**Jan 18, 2017: Mathematical Physics seminar, Perimeter Institute for theoretical physics, Canada.**Oct 31-Nov 4, 2016: BICMR/IBS-CGP joint Symplectic Geometry Workshop, Jeju, Korea.**Aug 6-11, 2016: The 7th International Congress of Chinese Mathematicians (Plenary talk), Beijing, China.**Aug 1-5, 2016: Strings 2016 (Parallel talk), Beijing, China.**June 20-26, 2016: Retrospective Workshop for the Thematic Program on Calabi-Yau Varieties: Arithmetic, Geometry and Physics, Herstmonceux Castle, UK**May 8-14, 2016: Lecture series for ``Factorization Algebras and Functorial Field Theories", MFO, Germany.**May 6-8, 2016: Simons Workshop on SYZ Mirror Symmetry and related topics, Harvard, USA.**Apr 24-30, 2016: Mini course on ``BV quantization and geometric applications", IBS-CGP, Korea.**Apr 5-12, 2016: MIST IV: Mathematics Inspired by String Theory, CUHK, Hong Kong.**Jan 1-4, 2016: Workshop on Poisson Geometry and Mathematical Physics, Chern Institute of Mathematics, Tianjin.**Dec 31, 2015: Strings-Math 2015 (Plenary talk), Sanya, China.**Dec 27, 2015: Workshop on Mathematics Physics, Dec 27, Sanya, China.**Nov 24, 2015: 2015 Annual Conference of Chinese Mathematical Society, CNU, Beijing.**Nov 14, 2015: Geometry and Physics seminar, Shanghai Jiaotong University, Shanghai**July 13-July 18,, 2015: ``Uniformization, Riemann-Hilbert Correspondence, Calabi-Yau manifold, and Picard-Fuchs Equation", Mittag-Leffler Institute, Sweden**July 6-10, 2015: GAP XII-Derived Algebraic Geometry, IBS-CGP, Pohang, Korea**March 28, 2015: Tianyuan workshop in algebraic geometry, AMSS, Beijing.**March 23, 2015: Symplectic Geometry and Mathematical Physics, Peking University**March 7, 2015: Beijing Geometry and Physics Colloquium, Peking University**Feb 7, 8, 2015: Lectures: Introduction to perturbative field theory, Morningside Center for Mathematics, CAS, Beijing.**Jan 20, 2015: String/Math seminar, Perimeter Institute for theoretical physics, Canada.**Oct 20, 2014: Geometry seminar, Lehigh University, USA.**Oct 6, 2014: Informal mathematical physics seminar, Columbia University, USA.**Sep 29-Aug 3, 2014: Homological methods in quantum field theory, Simons center for geometry and physics, USA.**Sep 18, 2014: Seminar on mathematical physics, Morningside Center for Mathematics, CAS, Beijing.**Aug 26, 2014: China annual complex analysis conference, USTC**Aug 5, 2014: 60 years of Calabi conjecture-Workshop in Honor of Professor Shing-Tung Yau on the occasion of his 65th birthday, Tsinghua University**June 8-15, 2014: Lecturer for Research Training Group 1670, University of Hamburg, Germany \item May 19-23, 2014: Representation Theory, Integrable Systems, and Quantum Fields, Northwestern University, USA**April 1, 2014: Algebraic geometry seminar, Princeton, USA**Mar 3-7, 2014: Workshop on B-model aspect of Gromov-Witten theory, University of Michigan**Feb 10-14, 2014: Lecturer: Primitive forms and related subjects, Kavli IPMU, Japan**Nov 25, 2013: Geometry and Physics seminar, University of Michigan, USA**July 22, 2013: Invited seminar, Kavli IPMU, Japan**July 16, 2013: The Sixth International Congress of Chinese Mathematicians, Taipei**Apr 12-14, 2013: Mini-course for FRG Workshop on Gromov-Witten theory, Columbia University, USA**Mar 11, 2013: Geometry and Physics seminar, University of Michigan, USA**Jan 29, 2013: Differential geometry seminar, Harvard University, USA**Nov 30, 2012: Everytopic Seminar, Brandeis University, USA**Nov 27, 2012: GAP Seminar, Penn State University, USA**Sep 14-17, 2012: Boston-Keio Summer Workshop on Geometry, Boston University, USA**Aug 27, 2012: FRG Workshop: Generalized Geometry, String Theory, and Deformations, Harvard University, USA**August 20-24, 2012: The Conference of Mirror Symmetry and Related Topics, KMUST, China**July 27-Aug 20, 2012: Summer course, MSC at Tsinghua University, China**August 10, 2012: Math Literature Seminar, MSC at Tsinghua University, China**July 18, 2012: Workshop on the mathematical aspects of quantum field theory, USTC, China**June 26, 2012: Geometry and Physics of the Landau-Ginzburg Model, IPMU, Japan**June 18, 2012: Quantization and Mathematics: An Undergraduate Conference, Northwestern University, USA**Mar 19, 2012: Geometry and Physics Seminar, University of Michigan, USA**Feb 18, 2012: Hong Kong Geometry Colloquium, Hong Kong**Feb 17,20, 2012: Geometry and Physics Seminar, HK Chinese Univ, Hong Kong**Feb 8,11, 2012: Geometry Seminar, HKUST, Hong Kong**Dec 9, 2011: Geometry Seminar, Boston University, USA**Nov 3, 2011: Felix Klein Seminar, University of Notre Dame, USA**Aug 3, 2011: Workshop on Chiral Differential Operators, Northwestern University, USA**July 19, 2011: Seminar on QFT, MIT, US**May 5, 2011: Mirror Symmetry Seminar, Simons Center for Geometry And Physics, Stonybrook**Mar 4, 2011: Algebraic Geometry Seminar, University of Wisconsin, USA**Feb 22, 2011: Differential Geometry Seminar, Harvard University, USA**Oct 14, 2010: Geometry/Physics Seminar, Northwestern University, USA**Sep 28, 2010: Differential Geometry Seminar, Harvard University, USA**Dec 4 2009: Differential Geometry Seminar, Harvard University, USA**Mar 12, 2009: Graduate Trivial Notion Seminar, Harvard University, USA**Apr 24, 2008: Graduate Trivial Notion Seminar, Harvard University, USA*