Mathematics Colloquium
Thursday, 14 December at 5.15 PM
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Venue: Ramanujan Hall
Host: Sudhir Ghorpade
Speaker: Mahir Bilen Can
Affiliation: Tulane University, New Orleans
Title: Symmetric spaces, Hessenberg varieties, and Wonderful Compactifications
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 to 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.