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Bin Gui

Assistant Professor, Yau Mathematical Sciences Center, Tsinghua University

Basic Information

Email
bingui (at) tsinghua.edu.cn
Office
Shuangqing Complex Building C648
Personal Website
binguimath.github.io

Research Areas

Two-dimensional conformal field theory, vertex operator algebras, conformal nets, algebraic quantum field theory, and tensor categories.

Education

  • 2009-2013, B.S., Shanghai Jiao Tong University.
  • 2013-2018, Ph.D., Vanderbilt University.

Employment

  • 2021-present, Assistant Professor, Yau Mathematical Sciences Center, Tsinghua University.
  • 2018-2021, Postdoctoral Fellow, Rutgers University.

Research Summary

Bin Gui studies the mathematical foundations of two-dimensional conformal field theory, especially the relation between algebraic vertex-operator-algebra methods and analytic conformal-net methods. His recent work develops analytic conformal blocks for C2-cofinite vertex operator algebras, including propagation, sewing, factorization, and positivity properties of fusion products. A central goal is to make the passage between VOA module categories and conformal nets precise enough that unitarity, tensor-category structure, and analytic CFT constructions can be compared within one framework.

Representative Publications

  • B. Gui, “Unitarity of the modular tensor categories associated to unitary vertex operator algebras, I,” Comm. Math. Phys. 366 (2019) 333-396.
  • B. Gui, “Unitarity of the modular tensor categories associated to unitary vertex operator algebras, II,” Comm. Math. Phys. 372 (2019) 893-950.
  • B. Gui, “Energy bounds condition for intertwining operators of type B, C, and G_2 unitary affine vertex operator algebras,” Trans. Amer. Math. Soc. 372 (2019) 7371-7424.
  • B. Gui, “Unbounded field operators in categorical extensions of conformal nets,” arXiv:2001.03095.
  • B. Gui, “Convergence of sewing conformal blocks,” arXiv:2011.07450.
  • B. Gui, “Categorical extensions of conformal nets,” Comm. Math. Phys. 383 (2021) 763-839.
  • B. Gui, “Q-systems and extensions of completely unitary vertex operator algebras,” Int. Math. Res. Not. IMRN.
  • B. Gui, “Bisognano-Wichmann property for rigid categorical extensions and non-local extensions of conformal nets,” Ann. Henri Poincare.

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