# Algebra and Number Theory Seminar Fall 2018

**Friday October 12th, 2018**

**TBA**

**Friday October 19th, 2018**

**TBA**

**Friday October 26th, 2018**

**James Cameron, University of California Los Angeles**

*Local cohomology modules of group cohomology rings via topology*

I'll describe how to use constructions from equivariant cohomology to study the local cohomology modules of group cohomology rings. In special cases, this leads to a description of local cohomology in terms of Tate cohomology. As an application, we compute the top several local cohomology modules of the cohomology of a p-Sylow of S_p^n. These computations show that the highest nonzero terms in these modules occur in lower degrees than guaranteed by the general theory.

**Friday November 2nd, 2018**

**TBA**

**Friday November 9th, 2018**

**Johan Steen, University of California Santa Cruz**

**A representation theoretic approach to multi-parameter clustering****In recent years, several fields in mathematics have sprung up in order ****to deal with the analysis of large data sets. Topological data analysis ****(TDA) is one such field. It provides ways of assigning topological ****invariants to discrete data sets, and the most common approach is by way ****of “persistent homology”: From a point cloud one produces a topological ****descriptor called the “bar code”, which equivalently is read off of the ****(very simple) representation theory of a totally ordered poset.****Unfortunately, multi-parameter persistent homology does not admit such a ****nice descriptor. In joint work with Ulrich Bauer (Munich), Magnus ****Botnan (Amsterdam) and Steffen Oppermann (Trondheim), we find that there ****is a representation theoretic reason for this, even for the simplest ****variant of persistent homology (namely clustering). In fact, we ****construct a general equivalence of categories which we apply to the ****setting of multi-parameter clustering.****Even though the main goal of this talk is to explain the abstract ****result, we will not lose sight of the motivating examples coming from TDA.**

**Friday November 16th, 2018**

**TBA**

**Friday November 23rd, 2018**

**TBA**

**Friday November 30th, 2018**

**Cameron Franc, University of Saskatchewan**

**Modular forms of rank 4 and level 1****Vector valued modular forms are holomorphic modular forms that transform according to,and take values in, a representation of the modular group. Being a discrete group, representations of the modular group live in complex analytic families, and in nice cases one can find corresponding families of vector valued modular forms. In this talk we'll recall some past work (joint with Geoff Mason) on what occurs in ranks 2 and 3, and then we'll discuss recent joint work with Geoff Mason on rank 4. The idea is to use functorial constructions, such as tensor products, symmetric powers and induction, to construct families of modular forms of rank 4.**

**Friday December 7th, 2018**

**TBA**