Total positivity: combinatorics, geometry and representation theory

Speaker: 何旭华教授，香港大学

Inviter: 数学所

Title:Total positivity: combinatorics, geometry and representation theory

Language: Chinese

Time & Venue: 2024.06.05 10：30-11：30  N202

Abstract: An invertible matrix is called totally positive if all its minors are positive. In 1994, Lusztig developed the theory of total positivity for arbitrary split real reductive groups and their flag manifolds. He further generalized the theory to arbitrary Kac-Moody groups in 2019. The theory of total positivity has found important applications in different areas: cluster algebras, higher Teichmuller theory, the theory of amplituhedron in physics, etc.In this talk, we will discuss some remarkable combinatorial, geometric and representation-theoretic aspects of total positivity. This talk is based on some recent works with Huanchen Bao.