Date : Sep. 24. 2021
Place : SNU
Speaker : 조윤형(SKKU)
TItle : Smoothing of Fano varieties and mutations
Let X be a smooth Fano variety. It was conjectured that if Y and Z are two Q-Gorenstein toric Fano varieties having the same good smoothing X, then Y and Z are related by a sequence of mutations. In this seminar, we discuss the case when X is a projective plane or a full flag variety (if time permits).
Title: Quasisymmetric functions, noncommutative symmetric functions, and weak Bruhat interval modules of 0-Hecke algebras
Symmetric functions have two generalizations: quasisymmetric functions and noncommutative symmetric functions. In 1996, Duchamp et al. introduced representation theoretical interpretations of these functions in terms of 0-Hecke algebras. In this talk, I will first explain these interpretations and related results. Then, I will introduce weak Bruhat interval modules of 0-Hecke algebras and their structural properties.