I work in the field of mathematical physics and am interested in algebraic and geometric aspects of quantum field theory and string theory.
Expositions
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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.
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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.
Publications
- Regularized Integrals on Elliptic Curves and Holomorphic Anomaly Equations
(with J. Zhou). Commun. Math. Phys. 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
- Regularized Integrals on Riemann Surfaces and Modular Forms
(with J. Zhou). Commun. Math. Phys. 388, 1403–1474 (2021).
- Vertex algebras and quantum master equation . To appear in J.Diff.Geom.
- 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.
- On the B-twisted topological sigma model and Calabi-Yau geometry (with Q.Li). J.Diff.Geom. 102 (2016) no.3, 409-484.
- A mirror theorem between Landau-Ginzburg models . Nuclear Phys. B., 898 (2015).
- On the B-twisted quantum geometry of Calabi-Yau manifolds (with Q. Li), Proceedings of the
Sixth International Congress of Chinese Mathematicians 2013.
- 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.
- 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
Preprints
- Quadratic Duality for Chiral Algebras
(with Z. Gui, K. Zeng), arXiv:2212.11252 [math.QA]
- Elliptic Trace Map on Chiral Algebras (with Z. Gui), arXiv:2112.14572 [math.QA]
- Twisted supergravity and its quantization (with K. Costello),arXiv:1606.00365[hep-th]
- Quantization of open-closed BCOV theory, I (with K. Costello), arXiv:1505.06703[hep-th]
- 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].
- Quantum BCOV theory on Calabi-Yau manifolds and the higher genus B-model (with K.Costello), arXiv:1201.4501[math.QA] .
- 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]
Invited talks
- 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