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
