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Si Li

Professor, Yau Mathematical Sciences Center / Department of Mathematical Sciences, Tsinghua University

Basic Information

Email
sili (at) tsinghua.edu.cn
Office
Jing Zhai 307

Research Areas

Mathematical physics; algebraic and geometric structures in quantum field theory and string theory; topological strings, BCOV theory, Landau-Ginzburg mirror symmetry, chiral algebras, and homotopical/derived methods in field theory.

Education

  • 1999-2003, B.S. in Physics, Special Class for the Gifted Young, University of Science and Technology of China.
  • 2003-2006, M.S. in Mathematics, University of Science and Technology of China.
  • 2006-2011, Ph.D. in Mathematics, Harvard University.

Employment

  • 2014-present, Professor, Department of Mathematical Sciences and Yau Mathematical Sciences Center, Tsinghua University.
  • 2012-2014, Assistant Professor, Department of Mathematics and Statistics, Boston University.
  • 2011-2012, Postdoctoral Fellow, Department of Mathematics, Northwestern University.

Research Summary

Si Li works on mathematical quantum field theory, geometric quantization, and algebraic structures in string theory. His recent work develops chiral-algebraic and homological tools such as quadratic duality, Hochschild homology, contact-term algebras, and Dijkgraaf's master equation, while also studying Chern-Simons matrix models and their large-N limits. Together with work on Picard-Lefschetz theory, alien calculus, and topological quantum mechanics on orbifolds, this program aims to make perturbative and nonperturbative structures of quantum field theory precise in geometric and algebraic terms.

Representative Publications

  • K. Costello, S. Li, “Quantization of open-closed BCOV theory, I,” and related work on BCOV theory and topological strings.
  • S. Li, “Calabi-Yau geometry, primitive forms and mirror symmetry,” and related work on Landau-Ginzburg mirror symmetry.
  • S. Li, “Vertex algebras and quantum master equation,” J. Differential Geom. 123 (2023) 461, arXiv:1612.01292.
  • K. Costello, S. Li, “Anomaly cancellation in the topological string,” Adv. Theor. Math. Phys. 24 (2020) 1723, arXiv:1905.09269.
  • W. He, S. Li, X. Tang, P. Yoo, “On the L2-Hodge theory of Landau-Ginzburg models,” Commun. Math. Phys. 379 (2020) 327.
  • Z. Gui, S. Li, “Elliptic Trace Map on Chiral Algebras,” arXiv:2112.14572.
  • S. Hu, S. Li, D. Ye, Y. Zhou, “Quantum Algebra of Chern-Simons Matrix Model and Large N Limit,” arXiv:2308.14046.
  • Z. Gui, S. Li, K. Zeng, “Quadratic duality for chiral algebras,” Adv. Math. 451 (2024) 109791, arXiv:2212.11252.

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