# Integrable systems around the world, September 14-16, 2020

Sep 14 – 16, 2020
SISSA
Europe/Rome timezone

## Differential Geometry of Orbit space of Extended Affine Jacobi Group $A_1$\$

Sep 15, 2020, 12:00 PM
30m
Chairman: Gregorio Falqui

#### Chairman: Gregorio Falqui

Scientific Programme

### Speaker

Guilherme Almeida

### Description

Dubrovin Frobenius manifolds are the geometric interpretation of a remarkable system of differential equations, called WDVV equations. Since the beginning of the ninethies, there has been a continuous exchange of ideas from fields that are not trivially related to each other, such as: string theory, non-linear waves, singularity theory, reflection groups and its extensions, random matrices theory, integrable systems, and Painleve equations. Dubrovin Frobenius manifolds theory has demonstrated to be thebridge between them.
Orbit space of reflection groups and its extensions are one of the main exam-
ples of Dubrovin Frobenius manifolds. In this talk, we define certain extensions of Jacobi groups of A1, prove an analogue of Chevalley Theorem for their invariants, and construct a Dubrovin Frobenius structure on it orbit spaces. This seminar is based on the results of arXiv:1907.01436v3, and arXiv:2004.01780v1.

### Primary author

Guilherme Almeida