Colloquium Lectures

Time: 9h30, Friday, June  16, 2017
Venue: Room 301, Building A5, Institute of Mathematics, VAST, 18 Hoang Quoc Viet, Cau Giay, Ha Noi.
Abstract: Convexity is an interesting and important phenomenon in Lie theory and symplectic geometry, because it links geometric properties to combinatorial invariants and, at the same time, it provides a framework for the classification of dynamics with symmetry. This talk is based on joint work with Tudor Ratiu, and consists of three parts:

• The first part is a brief review of classical convexity theorems, from Shur-Horn theorem about the diagonals of unitary matrices to Kostant's convexity theorem in Lie theory to Atiyah-Guillemin-Sternberg's and Kirwan's theorems on convexity of Hamiltonian compact group actions on symplectic manifolds, and various extensions.
• The second part is about what Tudor Ratiu and I did separately concerning convexity in symplectic geometry.
• The third part of the talk is about what we have been working with Tudor Ratiu very recently on convexity of integrable Hamiltonian systems on (pre)symplectic manifolds, also in the presence of focus-focus singularities.