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Categorifying quantum loop algebras

Abstract

The idea of categorification provides better understanding of rich structures associated with quantum groups and provides links between different representation categories. In this talk, we will explain an equivalence between a category of representations of quiver Hecke algebras for the Kronecker quiver and the category of equivariant perverse coherent sheaves on the nilpotent cone of type A. Both of them provides categorification of certain part of the quantum loop algebras of sl_2.

 

报告人简介

单芃,清华大学丘成桐数学科学中心教授,从事几何表示论方向的研究。2011年在巴黎第七大学取得博士学位。毕业后就职于法国国家科学研究中心,任副研究员,曾分别在卡昂大学、MIT、南巴黎大学开展研究工作。2017年底全职回到清华大学工作。曾获求是杰出青年学者奖,在 J. Amer. Math. Soc., Invent. Math.,Duke Math. J. 等数学顶级杂志上发表多篇高水平学术论文。