Welcome to my homepage

About me

I am now an assistant professor at Tsinghua University, Yau Mathematical Sciences Center.

My name in Chinese: 归斌/歸斌

Email:
binguimath(at)gmail(dot)com
bingui(at)tsinghua(dot)edu(dot)cn

Google Scholar

arXiv webpage

Academic Experiences

• (2021.9-) Assistant Professor, Yau Mathematical Sciences Center, Tsinghua University
• (2018.9-2021.6) Postdoc (Hill Assistant Professor), Math Department, Rutgers University-New Brunswick. Mentor: Yi-Zhi Huang
• (2013.8-2018.6) Ph.D., Math Department, Vanderbilt University. Advisor: Vaughan Jones
• (2009.9-2013.6) B.S., Zhiyuan College, Shanghai Jiaotong University. Advisors: Jin Liang, Yijun Yao

Research Interests

I'm interested in the mathematical areas that are related to two-dimensional Conformal Field Theory, including: Algebraic Quantum (Conformal) Field Theory, Vertex Operator Algebras, Subfactors and Von Neumann Algebras, Tensor Categories.

I consider myself a half-operator algebraist and half-vertex algebraist. I'm especially interested in the interplay between the operator algebraic (more precisely speaking, von Neumann algebraic) and the vertex algebraic approaches to 2d conformal field theory.

Courses

• (2022 Spring) Vertex Operator Algebras, Conformal Blocks, and Tensor Categories

Publications and Preprints

The following articles are listed in the order they were finished and submitted to arXiv. The arXiv indentifiers (YYMM.NNNNN) indicate the time of submission. Note that the preprints on this website might be more updated than the arXiv versions.

• Unitarity of The Modular Tensor Categories Associated to Unitary Vertex Operator Algebras, I, Comm. Math. Phys., (2019) 366(1), pp.333-396. arXiv:1711.02840 Preprint Typos

• Unitarity of The Modular Tensor Categories Associated to Unitary Vertex Operator Algebras, II, Comm. Math. Phys., (2019) 372: 893-950. arXiv:1712.04931 Preprint

• 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. arXiv:1809.07003 Preprint

• Categorical Extensions of Conformal Nets, Comm. Math. Phys., 383, 763-839 (2021). arXiv:1812.04470 Preprint (A talk with slides)

• Q-systems and extensions of completely unitary vertex operator algebras, to appear in Int. Math. Res. Not. IMRN. arXiv:1908.03484 Preprint

• Bisognano-Wichmann Property for Rigid Categorical Extensions and Non-local Extensions of Conformal Nets, Ann. Henri Poincaré, 22, 4017-4062 (2021). arXiv:1912.10682 Preprint

• Unbounded Field Operators in Categorical Extensions of Conformal Nets, submitted. arXiv:2001.03095 Preprint

• Regular Vertex Operator Subalgebras and Compressions of Intertwining Operators, J. Algebra, (2020) 564. 32-48. arXiv:2003.02921 Preprint

• Polynomial Energy Bounds for Type F_4 WZW-models, Internat. J. Math., Vol. 31, No. 12 (2020). arXiv:2004.02064 Preprint

• Convergence of Sewing Conformal Blocks, submitted. arXiv:2011.07450 Preprint

• Sewing and Propagation of Conformal Blocks. arXiv:2110.04774 Preprint

• Genus-zero Permutation-twisted Conformal Blocks for Tensor Product Vertex Operator Algebras: The Tensor-separable Case. arXiv:2111.04662 Preprint Slides

• On a Connes Fusion Approach to Finite Index Extensions of Conformal Nets. arXiv:2112.15396 Preprint

Notes

• Conformal Blocks: Vector Bundle Structures, Sewing, and Factorization

In this monograph we give a complex-analytic approach to the theory of conformal blocks for VOAs. Part of this note has been adapted to form the main body of my article Convergence of Sewing Conformal Blocks. The section on (multi) propagation of conformal blocks has been expanded and explained in more details in the article Sewing and Propagation of Conformal Blocks.

• Spectral Theory for Strongly Commuting Normal Closed Operators

We give a detailed and self-contained exposition of the topics indicated in the title of this monograph.