Abstract:

Categorification is the process of finding hidden higher level structure. In this talk, I will introduce a new class of algebra, which is called the shifted q=0 affine algebra. Our motivation comes from the categorification of quantum groups and their actions on categories. Then I will explain how the shifted q=0 affine algebra acts on categories by using the language of Fourier-Mukai transformations. The kernels are induced by natural correspondences on the bounded derived categories of coherent sheaves on Grassmannians or partial flag varieties. Finally, if time permits, I may discuss some further directions.