[BIMSA-Tsinghua Quantum Symmetry Seminar] Forest groups

 

Speaker:  Arnaud Brothier

Time:     10:30-12:00

Date:       2022/07/22

Zoom: 638 227 8222    Passcode: BIMSA

 

Abstract: 

In his quest in constructing conformal field theories (CFT) from subfactors Vaughan Jones found an unexpected connection with Richard Thompson's group. This led among others to beautiful new connections with knot theory and to Jones' technology: an efficient theory for constructing actions of groups constructed from categories.
I am proposing a program in the vein of Jones' work but where Thompson's group is replaced by a family of groups that I name "forest groups". These groups are constructed from planar diagrams. They capture key aspects of the Thompson group but also aim to better connect subfactors with CFT. They are tailor-made for using Jones' technology admitting powerful skein theoretical descriptions. Apart from strengthening Jones' vision our program produces a plethora of explicit groups satisfying interesting and rare properties.
I will briefly explain the discovery of Jones and present forest groups. Explicit examples will be given as well as concrete applications in group theory. No previous knowledge on subfactors, CFT, nor group theory is required for following this talk.


Reference: https://arxiv.org/abs/2207.03100

 

Speaker Intro:

I am a French researcher in mathematics. I grew up in France and quickly decided to become a mathematician. All my course work was done there. My doctorate was co-supervised by Vaughan Jones in UC Berkeley and Andrzej Zuk in Paris VII. After various postdocs (in KU Leuven, Vanderbilt, and Rome) I went to UNSW Sydney where I obtained tenure. My research has been initially about Jones' subfactors and analytic questions in von Neumann algebras. Since 2016 I have shifted my research toward a fascinated connection than Jones made between subfactors, conformal field theory, and Richard Thompson's groups. I enjoy learning new mathematics and took Jones' connections as an opportunity to discover new fields. I am now learning, using, and applying ideas from and to subfactors, operator algebras, and group theory.
Beside mathematics I am passionate about antiquity and kitesurfing!