We start by relating a result on the reducibility of induced representations of a reductive group through local Langlands correspondence to Artin L-functions. Such a result is of interest in the study of the arithmetic theory of intertwining...

#
special seminar

New kinds of vortex sheets with vorticity confined to the boundary layer are proposed and investigated in detail. Exact solutions of the steady Navier-Stokes equations for a planar vortex sheet in arbitrary background strain are found in terms of...

Given a finite graph, the arboreal gas is the measure on forests (subgraphs without cycles) in which each edge is weighted by a parameter β>0. Equivalently this model is bond percolation conditioned to be a forest, the independent sets of the graphic...

### Existence of an unbounded nodal hypersurface for smooth Gaussian fields in dimension d > 2

For the Bargmann--Fock field on Rd with d>2, we prove that the critical level lc(d) of the percolation model formed by the excursion sets {f≥l} is strictly positive. This implies that for every l sufficiently close to 0 (in particular for the nodal...

In this talk I will describe a topological approach to some problems about algebraic functions due to Klein and Hilbert. As a sample application of these methods, I will explain the solution to the following problem of Felix Klein: Let $\Phi_{g,n}$...

Given a polynomial in one variable, what is the simplest formula for the roots in terms of the coefficients? Hilbert conjectured that for polynomials of degree 6,7 and 8, any formula must involve functions of at least 2, 3 and 4 variables...

I will describe the problem of finding the homotopy type of the space of quantum Hamiltonians in dimension d under certain constraints. The common assumptions are that the interactions have finite range and that the ground state is separated from...

\[ x_1^2 + x_2^2 + \cdots + x_n^2 = ax_1x_2 \cdots x_n + k.\]

In this talk, we establish an asymptotic count for the number of...