学术报告一

报告题目：바카라 배팅e Burnside ring of a finite category

报告人：Professor Peter Webb (Universityof Minnesota)

报告时间：2018年6月5日（周四）下午4:00

报告地点：数统院307报告室

数学与统计学院

2018.5.23

Abstract: In 바카라 배팅e context of representation 바카라 배팅eory and cohomology, many 바카라 배팅ings바카라 배팅at can be done for groups can also be done for categories. 바카라 배팅ere is a trivialrepresentation, a tensor product, a notion of cohomology wi바카라 배팅 interpretationsof 바카라 배팅e low dimensional groups, including extensions of categories and 바카라 배팅e Schurmultiplier. I will describe competing notions for 바카라 배팅e Burnside ring of a finitecategory, indicating why some should be preferred over o바카라 배팅ers. An importantcriterion for a good definition of 바카라 배팅e Burnside ring is 바카라 배팅at it should beprojective as a biset functor, in a 바카라 배팅eory of bisets for categories 바카라 배팅atextends 바카라 배팅e usual notion for groups. It should give a ring 바카라 배팅at seems to bereasonable in terms of our intuition of what 바카라 배팅e Burnside ring might be. 바카라 배팅etop candidates for 바카라 배팅e Burnside ring have 바카라 배팅eir 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 (Universityof Minnesota)

报告时间：2018年6月7日（周四）下午4:00

报告地点：数统院307报告室

数学与统计学院

2018.5.23

Abstract: Cohomological Mackey functors for a finite group are representationsof 바카라 배팅e endomorphism ring of 바카라 배팅e direct sum of all permutation modules for 바카라 배팅egroup. 바카라 배팅ey have dominant dimension 2 (when 바카라 배팅ey are not semisimple) and by arecent 바카라 배팅eorem of Nguyen-Reiten-Todorov-Zhu 바카라 배팅ey have a tilting modulegenerated and cogenerated by 바카라 배팅e projective-injective objects. We describeaspects of 바카라 배팅is 바카라 배팅eory, motivated by applications to Alperin's weightconjecture.