BIMSA Mini-Course (Beijing, 2024-04-16)
Speaker: Yasuyuki Kawahigashi (The University of Tokyo)

Title
Operator algebras, bi-unitary connections and tensor networks - Session 1/4

Abstract
Tensor categories have emerged as a new type of "quantum symmetry" generalizing classical group symmetry in various fields of mathematics and physics such as quantum groups, quantum topological invariants, quantum information, vertex operator algebras, conformal field theory and topological order in condensed matter physics. The Jones theory of subfactors in operator algebras give a powerful method to study such symmetries. A bi-unitary connection is a tool to describe such tensor categories using finite dimensional unitary matrices and particularly suited to study tensor networks in 2-dimensional topological order. I will present this theory without assuming knowledge on operator algebras.

References
Kawahigashi, Yasuyuki. Projector matrix product operators, anyons and higher relative commutants of subfactors. Math. Ann. 387 (2023), no. 3-4, 2157--2172
Evans, David E.; Kawahigashi, Yasuyuki. Subfactors and mathematical physics. Bull. Amer. Math. Soc. (N.S.) 60 (2023), no. 4, 459--482.
Evans, David E.; Kawahigashi, Yasuyuki. Quantum symmetries on operator algebras. Oxford Mathematical Monographs. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1998. xvi+829 pp.

Video
https://bimsa.net/bimsavideo.html?id=...

Speaker Introduction
Yasuyuki Kawahigashi is a distinguished mathematician renowned for his contributions to operator algebras, mathematical physics, and particularly in the intricate realm of conformal field theory (CFT). His expertise extends to the study of subfactors, shedding light on the mathematical structures underpinning quantum theories. Kawahigashi's work explores the interplay between mathematics and theoretical physics, offering profound insights into operator algebras arising in quantum field theory and statistical mechanics.

Speaker Homepages
https://www.ms.u-tokyo.ac.jp/~yasuyuk...
https://www.s.u-tokyo.ac.jp/en/people...

Webpage of the Mini-Course
https://www.bimsa.cn/newsinfo/914094....

Playlist of the Mini-Course:
   • Yasuyuki Kawahigashi - Operator algeb...