题目: Geometric, cohomological, and motivic approach to Hall algebras.
      报告人：林宗柱教授
      时间：2012年7月23日(星期一) 下午2：30—5：00
               2012年7月24日(星期二) 下午4：00—5：00

      地点：数学系致远楼108

摘要:
Abstract: Ringel defined Hall algebras for quivers and Green extended for more general hereditary algebras over finite fields by counting subrepresentations. Lusztig used his induction method for character sheaves and defined Hall algebras (rather composition algebras) as direct sums of the Grothendieck groups of certain categories of perverse sheaves (with shifts) on certain algebraic varieties. From these categories, the simple objects (concentrated at degree 0) form the canonical basis. Now there are more uniform approaches to Hall algebras in terms of equivariant cohomology of certain complex varieties related to quivers and in terms of motivic counting in algebraic geometry. Then counting over finite fields becomes one special case by simply applying the motivic measure of counting number of rational points over finite fields. In this series of lectures, I will review Ringels' definition and Lusztig's perverse sheave approach and then outline recent cohomological and motive approach by Kontsevich-Soibelman and many others. The latter approaches have other applications in physics. It time permits, I will also mention roles played by stability conditions on Hall algebrais.