|DATE||January 28 (Fri), 2022|
|TITLE||Semi-toric degenerations of Richardson varieties arising from cluster structures on flag varieties II|
|ABSTRACT||A toric degeneration is a flat degeneration from a projective variety to a toric variety, which can be used to apply the theory of toric varieties to other projective varieties. In the case of a flag variety, its toric degeneration with desirable properties induces degenerations of Richardson varieties to unions of irreducible toric subvarieties, called semi-toric degenerations. Semi-toric degenerations are closely related to Schubert calculus. For instance, Kogan?Miller constructed semi-toric degenerations of Schubert varieties from Knutson?Miller's semi-toric degenerations of matrix Schubert varieties which give a geometric proof of the pipe dream formula of Schubert polynomials. In the 1st talk, we review the notion of extended g-vectors in cluster theory, which induces Newton?Okounkov bodies and toric degenerations of a compactified cluster variety. In the 2nd talk, we discuss such Newton?Okounkov bodies and toric degenerations for a flag variety. We see that these induce semi-toric degenerations of Richardson varieties, which can be regarded as generalizations of Kogan?Miller's semi-toric degeneration. This series of talks is partly based on a joint work with Hironori Oya.
Meeting ID: 290 623 8932