2025년 11월 QSMS Monthly Seminar
- Date: Nov 28th (Fri) 14:00 ~ 17:00
- Place: 27-220 (SNU)
- Contents:
Speaker: 권재훈 (SNU)
Title: BGG category for simple Lie algebra of type A and quiver Hecke algebras
Abstract: This is an expository talk. The BGG category of a semisimple Lie algebra generalizes the category of its finite-dimensional representations, where the character formula for simple objects is given by the Kazhdan–Lusztig formula. In type A, Arakawa and Suzuki introduced a functor from the BGG category to the category of finite-dimensional representations of degenerate affine Hecke algebras of type A. In this talk, we review this functor and explain its connection to the representation theory of quiver Hecke algebras, along with some applications.
Speaker: 조윤형 (SKKU)
Title: Mutations of Fano simplices and Diophantine equations
Abstract: A combinatorial mutation of a lattice polytope is a procedure that produces a new lattice polytope, serving as the combinatorial counterpart of a mutation of Landau–Ginzburg mirrors on a Fano manifold. In this talk, we describe a cluster-type structure on a Fano simplex, the polar dual of the moment polytope of a fake weighted projective space. More precisely, we define the notion of a mutable facet of a Fano simplex and prove that the number of mutable facets (called the rank) is invariant under combinatorial mutation. Consequently, each Fano simplex gives rise to a rank-valent graph whose vertices and edges correspond to Fano simplices and mutations, respectively. In dimension two, we show that a Fano triangle is of full rank (i.e., three) if and only if the corresponding fake weighted projective plane admits only T-singularities.