Quantum Symmetries and Quantum Arithmetic

Speaker: Sebastien Palcoux

Date：Mon. &Tues. 2021-02-22~05-16, 15:20-16:55

Venue：BIMSA 1120 Room & Zoom ID：361 038 6975，Password：BIMSA

Abstract：

This mini-course will introduce to the Galois-like symmetries of von Neumann algebras: subfactor and planar algebra, analogous of field extension and Galois group, which highly generalizes the notion of (finite) quantum group.
In this framework, we will generalize Ore's theorem (about cyclic groups), extend the prime and natural numbers, generalize the Euler's totient function, and apply to the representation theory of finite groups.

References:

- Vaughan Jones, Von Neumann Algebras:

https://math.berkeley.edu/~vfr/MATH20909/VonNeumann2009.pdf

- Vaughan Jones and V.S. Sunder, Introduction to subfactors:

https://doi.org/10.1017/CBO9780511566219

- Vaughan Jones, Planar algebras, I:

https://arxiv.org/abs/math/9909027

- Sebastien Palcoux:

- Ore's theorem for cyclic subfactor planar algebras and beyond,

https://doi.org/10.2140/pjm.2018.292.203,

- Euler totient of subfactor planar algebras,

https://doi.org/10.1090/proc/14167

- Ore's theorem on subfactor planar algebras,

https://doi.org/10.4171/QT/141

- Dual Ore's theorem on distributive intervals of finite groups,

https://doi.org/10.1016/j.jalgebra.2018.03.017

Record：

1.Von Neumann Algebras

2.Subfactors

3.Planar Algebras

4.Quantum Arithmetic

Sildes