学术报告（一）

报告题目：The Burnside ring of a finite category

报 告 人：Professor Peter Webb（University of Minnesota）

报告时间：2018年6月5日  16:00

报告地点：数统院307报告室

报告摘要：

In the context of representation theory and cohomology, many thingsthat can be done for groups can also be done for categories. There is a trivialrepresentation, a tensor product, a notion of cohomology with interpretationsof the low dimensional groups, including extensions of categories and the Schurmultiplier. I will describe competing notions for the Burnside ring of a finitecategory, indicating why some should be preferred over others. An importantcriterion for a good definition of the Burnside ring is that it should beprojective as a biset functor, in a theory of bisets for categories thatextends the usual notion for groups. It should give a ring that seems to bereasonable in terms of our intuition of what the Burnside ring might be. Thetop candidates for the Burnside ring have their structure described to someextent by an extension of Burnside's marks homomorphism.

学术报告（二）

报告题目：Cohomological properties of cohomological Mackey functors

报 告 人：Professor Peter Webb（University of Minnesota）

报告时间：2018年6月7日  16:00

报告地点：数统院307报告室

报告摘要：

Cohomological Mackey functors for a finite group are representationsof the endomorphism ring of the direct sum of all permutation modules for thegroup. They have dominant dimension 2 (when they are not semisimple) and by arecent theorem of Nguyen-Reiten-Todorov-Zhu they have a tilting modulegenerated and cogenerated by the projective-injective objects. We describeaspects of this theory, motivated by applications to Alperin's weightconjecture.