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

*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).*Quadratic Duality for Chiral Algebras*(with Z. Gui, K. Zeng), arXiv:2212.11252 [math.QA]*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*