Vorträge in der Woche 24.06.2019 bis 30.06.2019

Dienstag, 25.06.2019: Singuläre Zusammenhänge und die reduzierte singuläre Instanton-Floer-Homologie, Teil II

Prof. Dr. Frank Loose (Universität Tübingen)

Dienstag, 25.06.2019: Arithmetic Quantum Unique Ergodicity II

Martin Meßmer

Mittwoch, 26.06.2019: Describing the Jelonek set of a polynomial map via Newton polytopes

Dr. Boulos El Hilany

A polynomial map f=(f_1,...,f_n): C^n --> C^n is said to be non-proper at a point p if the preimage of any compact neighbourhood of p is not compact. The set of all such points, called the Jelonek set of f, measures how far such a map is from being proper. I will restrict to a certain large class of maps f above and present a new method for computing the non-properness set that depends on the geometry of the corresponding Newton polytopes. This method is mostly combinatorial, leads to significantly faster computations, and holds true for the real case. With this approach, previously-known results can be deduced in an easier fashion as well as new applications arise.

Donnerstag, 27.06.2019: DPW Potentials for Compact Symmetric CMC Surfaces in the 3-Sphere

Benedetto Manca

Donnerstag, 27.06.2019: Convergence rates for the numerical approximation of the 2D stochastic Navier-Stokes equations

Dominic Breit, Heriot Watt University, Edinburgh

We study the stochastic Navier-Stokes equations in two dimensions with respect to periodic boundary conditions. The equations are perturbed by a nonlinear multiplicative stochastic forcing with linear growth (in the velocity) driven by a cylindrical Wiener process. We establish convergence rates for a finite-element based space-time approximation with respect to convergence in probability (where the error is measure in the $L^\infty_t(L^2)\cap L^2_t(W^{1,2}_x)-norm$). The main result provides linear convergence in space and convergence of order (almost) 1/2 in time. This improves earlier results from Carelli-Prohl, where the convergence rate in time is only (almost) 1/4. Our approach is based on a careful analysis of the pressure function using a stochastic pressure decomposition.

Donnerstag, 27.06.2019: Ancient solutions to the Ricci flow with rotational symmetry

Prof. Dr. Simon Brendle (Columbia University)

I will discuss our recent proof of Perelman's conjecture concerning the classification of singularity models in 3D Ricci flow. The proof consists of two parts: An argument reducing the general case to the rotationally symmetric case, and a classification of noncompact ancient solutions with rotational symmetry. In this lecture, I will focus on the latter part. The proof relies on a combination of several techniques, including an analysis of the linearized equation in the cylindrical region, a barrier argument, and the Harnack inequality