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About
President
Governance
Partner Institutions
Visit
People
Management
Faculty
Postdocs
Visiting Scholars
Staff
Administration
Academic Support
Research
Research Groups
Courses
Seminars
Join Us
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Forum
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Qiuzhen College, Tsinghua University
Yau Mathematical Sciences Center, Tsinghua University (YMSC)
Tsinghua Sanya International  Mathematics Forum (TSIMF)
Shanghai Institute for Mathematics and  Interdisciplinary Sciences (SIMIS)
BIMSA > YMSC-BIMSA Quantum Information Seminar Conformal blocks of C_2 cofinite vertex operator algebras
Conformal blocks of C_2 cofinite vertex operator algebras
Organizer
Zheng Wei Liu
Speaker
(Tsinghua) Hao Zhang
Time
Friday, April 14, 2023 9:30 AM - 10:30 AM
Venue
JCY-1
Online
Tencent 494 8360 9451 (2023)
Abstract
Vertex operator algebras (VOAs) are a mathematically rigorous formulation of 2d conformal field theory (CFT). In 2008, Yi-Zhi Huang proved a significant result that the representation category of a "rational" and "C_2 cofinite" VOA V (plus some minor assumptions) is a modular tensor category. Huang's proof relies on a deep understanding of the geometric properties of conformal blocks (a crucial concept in VOA) associated to compact Rieman surfaces of genera 0 and 1. In recent years, these geometric properties have also been proved for higher genus conformal blocks associated to C_2 cofinite and rational VOAs. However, much less was known for C_2 cofinite but non-rational VOAs. Indeed, only the genus-0 story was clear, which led to Huang-Lepowsky-Zhang's construction of braided tensor categories for the representations of C_2 cofinite VOAs. The categories are not necessarily semisimple since V is not assumed to be rational. In this talk, we present an ongoing project that gives a systematic approach to the geometric properties of conformal blocks of C_2 cofinite but non-rational VOAs, associated to compact Riemann surfaces of all genera. Our approach generalizes simultaneously Huang-Lepowsky-Zhang's tensor category theory and higher level Zhu's algebras.
Beijing Institute of Mathematical Sciences and Applications
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