Title : Localization of quiver Hecke algebras and open Richardsdon varieties

Abstract : By localizing a monoidal category consisting of modules over a quiver Hecke algebra, one can obtain an abelian monoidal category whose Grothendieck ring is isomorphic to the coordinate ring of the open Richardson variety. I will explain the definition of open Richardson varieties, categories of modules over quiver Hecke algebras, and the localization procedure for monoidal categories. Some properties of the resulting category will be discussed. This is a joint work with M. Kashiwara, S.-j. Oh, and E. Park.