# Colloquium abstracts

**Pinakinath Saha**

TIFR, Mumbai

October 8, 2020

**Automorphism groups of Schubert varieties and rigidity of Bott-Samelson-Demazure-Hansen varieties**: Throughout this talk, we assume $G$ to be a simple algebraic group of adjoint type over the field $mathbb{C}$ of complex numbers, $B$ to be a Borel subgroup of $G$ containing a maximal torus $T$ of $G.$ Let $G/B$ be the full flag variety consisting of all Borel subgroups of $G.$ For $w$ in $W,$ let $X(w)$ denote the Schubert variety in $G/B$ corresponding to $w.$ In this talk, we discuss the following three problems: Prob 1: Whether given any parabolic subgroup $P$ of $G$ containing $B$ properly, is there an element $w$ in $W$ such that $P=Aut^0(X(w))?$ Prob 2: Let $G =PSO(2n+1,mathbb{C})(n ge 3).$ Let $w$ be an element of the Weyl group $W$ and $underline{i}$ be a reduced expression of $w.$ Let $Z(w, underline{i})$ be the Bott-Samelson-Demazure-Hansen variety (the desingularization of $X(w)$) corresponding to $underline{i}.$ In this talk, we discuss the cohomology modules of the tangent bundle on $Z(w_{0}, underline{i}),$ where $w_{0}$ is the longest element of the Weyl group $