Seminar Announcement
Date: Tuesday, 28 November 2023
Time: 11:30 AM
Venue: Lecture Hall 1
Symmetric spaces and Hessenberg varieties
Mahir Bilen Can
Tulane University, USA.
28-11-23

---

Abstract

Symmetric spaces appear in various branches of mathematics and physics. Their origins go back to Cartan's influential work on Riemannian geometry. In this talk after briefly reviewing symmetric spaces and their origins, we will discuss a special family of Hessenberg varieties in relation with K-orbit closures in flag varieties, where K is the symmetric subgroup S(GL(k)xGL(n-k)) in SL(n). Our goal is to explain how K-orbits can be used for understanding the geometry of Hessenberg varieties of semisimple operators with two eigenvalues. If time permits, we will shift gears towards wonderful embeddings of Hermitian symmetric spaces. We will discuss some applications of regular SL(2) actions in this setting. Parts of this talk are based on my joint work with Martha Precup, John Shareshian, and Ozlem Ugurlu.