Speaker: Mahir Bilen Can (Tulane)

Title: Symmetric Spaces: Origins, Generalizations, and Applications

Abstract: Symmetric spaces, which have silently shaped the landscape of mathematics for centuries, came into the spotlight thanks to the pioneering work of Elie Cartan. These spaces have intrinsic connections to harmonic analysis, algebraic geometry, mathematical physics, combinatorics, representation theory.. In this talk, we will gently introduce the concept of symmetric spaces and briefly review some of their examples and classifications. Then, we will discuss their fascinating natural generalizations, namely, spherical varieties. Finally, we will present some of our recent research, which has arisen from a natural combinatorial application of these generalizations of symmetric spaces. While the tone of our talk will be algebraic, we do not assume any prior background in the subject.