Speaker: Patrick Brosnan
Affiliation: University of Maryland, USA
Title of Talk: The geometry of Hessenberg and Lusztig varieties
Date: January 21, 2026
Time: 14:30:00 Hours
Venue: Guest House Seminar Room

Abstract: Hessenberg and Lusztig varieties are two families of closed subvarieties of generalized flag varieties with representation theoretic significance. In the case of Hessenberg varieties, one associates to a combinatorial piece of data a family of varieties living over the Lie algebra of a reductive group $G$. (For the general linear group, that combinatorial piece of data is just an integer-valued function. In general, it can be thought of as a $G$-equivariant subbundle of the tangent bundle of the flag variety.) In the case of Lusztig varieties, one associates to each element of the Weyl group of $G$ a family of varieties over $G$. I'll talk about some basic results on the geometry of Hessenberg varieties. Then I'll state a theorem on the automorphisms of deformations of Hessenberg varieties. Finally, I'll state a theorem about the relationship between Hesssenberg and Lusztig varieties.