Geometry and Physics Seminar
Speaker : Peng Shan
Title: Categorification of quantum loop sl_2
Abstract: Categorification of quantum groups has important applications in representation theory and low dimensional topology.
In the first part, Situ Quan will give an introduction to quiver Hecke algebras and how to categorify negative part of quantum groups via their modules categories.
In the second part, I will explain a recent result on an equivalence of categories between a module category of quiver Hecke algebras associated with the Kronecker quiver and a category of equivariant perverse coherent sheaves on the nilpotent cone of type A. This provides a link between two different monoidal categorifications of the open quantum unipotent cell of affine type A_1.
Speaker : Mauricio Romo
Title : A GLSM view on Homological Projective Duality
Abstract : After an introduction to the concept of window categories of B-branes on gauged linear sigma models (GLSM) and of homological projective duality, I will present a rather general construction of homological projective dual pairs using gauged linear sigma models.
I will mostly focus on the abelian case and, if time permits, will present a few remarks for the nonabelian case. This is based on joint work with Z. Chen and J. Guo: 2012.14109