Speaker: Professor Emmanuel Lettellier

Affiliation: Universite Denis-Diderot (Paris 7)

## Abstract

The Deligne-Simpson problem is the following one: for which triple (C_1,C_2,C_3) of GL(n)-conjugacy classes of matrices does the equation

X_1+X_2+X_3=0 with X_i a matrix in C_i for i=1,2,3

have a solution ?

This problem was motivated by the analytic theory of linear systems of differential equations defined on the Riemann sphere. V. Kostov brought partial solutions to this problem around the end of the last century. Later, about 20 years ago Crawley-Boevey brought a beautiful answer to this problem in terms of "root systems" of star-shaped graphs. In this talk I will explain Crawley-Boevey's work and mention some recent applications in representation theory.

### About Pure mathematics seminars

We present regular seminars on a range of pure mathematics interests. Students, staff and visitors to UQ are welcome to attend, and to suggest speakers and topics.

Seminars are usually held on Tuesdays from 2 to 3pm.

Talks comprise 45 minutes of speaking time plus five minutes for questions and discussion.

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#### Contact us

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