Abstract: This talk will introduce spherical elements in a finite Coxeter system. These spherical elements are a generalization of Coxeter elements, that conjecturally, for Weyl groups, index Schubert varieties in the flag variety G/B that are spherical for the action of a Levi subgroup. We will see that this conjecture subsumes previous sphericality results for Schubert varieties in G/B due to P. Karuppuchamy, J. Stembridge, P. Magyar–J. Weyman-A. Zelevinsky. In type A, the combinatorics of Demazure modules and their key polynomials, multiplicity freeness, and split-symmetry in algebraic combinatorics are employed to prove this conjecture for several classes of Schubert varieties. This talk is based on joint work with Alexander Yong. Please email Colleen at cer2 (at) illinois (dot) edu for the Zoom ID and password.