Talk

Moments of Riemann zeta function have been studied extensively in analytic number theory. Some of these results have been extended to other classes of $L$-functions.
In this talk, we will report on some recent work concerning moments of a large class of $L$-functions. This is a joint work with Gaurav Kumar and Deep Thakur.
 

A global representation is a compatible collection of representations of the outer automorphism groups of the finite groups in a family U. These objects appear naturally in classical representation theory, in the study of representation stability, and in global homotopy theory. In this talk, I will present the key features of the theory, with a particular focus on aspects arising from tensor-triangular geometry.

A classical theorem of M. Hall states that every finitely generated subgroup of a free group is a free factor of a finite index subgroup. Moreover, the works of Brunner--Burns and Dunwoody, imply that any finitely presented group satisfying this M. Hall's property must be virtually free, i.e., it must have a finite index free subgroup. However, many virtually free groups fail to have M. Hall's property. In the talk I will discuss the result that a weaker property (LR), defined by Long and Reid, does holds in all virtually free groups.

Speakers:

1.

2.

3.

4.

5.

A matroid is a fundamental and actively studied object in combinatorics. Matroids generalize linear independence in vector spaces as well as many aspects of graph theory. After a short introduction to matroids, I will present parts of a new OSCAR module for matroids through several examples. I will focus on computing the moduli space of a matroid, which is the space of all arrangements of hyperplanes with that matroid as their intersection lattice.