Events

This will be an experimental “Jazz session” where both of us will be explaining our recent results together.
We’ll also be encouraging audience participation and are aiming not only at 4-manifolds experts.

There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:

The asymptotic behaviour of moments of L-functions is of special interest to number theorists and there
are conjectures that predict the shape of the moments for families of L-functions of a given symmetry type.
However, only some results for the first few moments are known. In this talk we will consider the asymptotic
behaviour of the first moment of the product of a Hecke L-function and a symmetric square L-function
in the weight aspect. This is joint work with  O. Balkanova, G. Bhowmik, D. Frolenkov. 

The rationality problem for smooth Fano threefolds over algebraically closed fields is basically solved.
In this talk I will discuss rationality  of forms of these  Fanos over nonclosed fields of characteristic 0.
I will concentrate on the case where the  Picard number  equals 1.

The talk is based on joint work with Alexander Kuznetsov (in progress).