Department of Mathematics

Title: Introduction to the trace formula.Abstract: This will be an introductory lecture to a very informal learning seminar that will run this semester. Topics will vary, but many of the talks will be related to the trace formula, which is one of the most important tools in the theory of automorphic representations. I will start […]

Title: Introduction to the trace formula. (Cont.)Abstract: In the first talk I presented some useful notions and translations in the theory of automorphic representations (Hecke operators and p-adic groups, locally symmetric spaces and adelic quotients, etc.). In this talk, I will give a general introduction to trace formulas, and some of the questions that we […]

Title: Speculations on Computing with the Relative Trace FormulaAbstract: I will discuss and motivate the problem of computing statistics of automorphic representations. Many statistics have been computed previously using "explicit" forms of Arthur's trace formula. I will present a very speculative plan to develop similar "explicit" versions of relative trace formulas and mention some new specific […]

Title: An introduction to Hopf Rings.Abstract: An old guy’s perspective on what homotopy theory used to be about and why complex cobordism has become central to the study.And, I’ll show one approach to getting more (and different) information about complex cobordism.If time permits (it won’t), I’ll show some of how chromatic homotopy theory comes out […]

Title: Relative trace formulae and progress on the mixed truncationAbstract: After a quick (re)introduction to relative trace formulae, we shall focus on the divergence issue in establishing them. We plan to survey known examples of the mixed truncation and discuss an ongoing work on trace formulae for infinitesimal symmetric spaces.