Testbrett

Aus betrieblichen Gründen entfällt heute die Hotlineschicht von 14:00 bis 15:30 in der Fliednerstraße. Unsere Hotline ist daher bis 15:00 erreichbar.

My talk shall be concerned with the problem of rigorous derivation of the macroscopic laws governing heat propagation from the microscopic models formulated in statistical mechanics. A classical microscopic model of the thermal energy transport is provided by a chain of coupled oscillators on the integer lattice, that describes atoms (or molecules) in a crystal. Establishing, in a mathematical precise way, such laws, by taking appropriate scaling limits, is the central problem of rigorous statistical mechanics. One of the tools used to conclude such results is to introduce some stochasticity inside the system. We summarise some of the results obtained recently concerning the derivation of the macroscopic heat equation from the microscopic behaviour of a harmonic chain with a stochastic perturbation. We focus our attention on the emergence of macroscopic boundary conditions. The results have been obtained in collaboration with Joel Lebowitz, Stefano Olla and Marielle Simon.

In den Spielregeln von "Tetris", "Sokoban", "Magic: The Gathering" und vielen anderen scheinbar harmlosen Spielen verstecken sich universelle Computer. Deshalb erweisen sich manche auf den ersten Blick einfache Fragen, die man sich zu diesen Spielen stellen könnte, als unentscheidbar. Prof. Edmund Weitz bietet mit seinem Vortrag eine "spielerische" Einführung in eines der berühmtesten Resultate der theoretischen Informatik und erklärt, warum Mathematikerinnen und Mathematiker so gerne spielen.

Tosio Kato's monumental work on perturbation theory of operators was highly motivated by applications to partial differential equations in non homogeneous media. For example, how is the propagation of waves affected by perturbation of its conductivity? The first attempts in the fifties were by functional analysis methods because it is expected that kinetic energy is related to spectrum. But they were not successful. The connection to harmonic analysis questions was made by A. McIntosh in the eighties. A complete solution occurred in the early 2000 and still implies nowadays unsuspected consequences. This talk will present some aspects of this story.

Extremal black holes are special solutions to the Einstein field equations characterized by maximal spin or charge relative to their mass. In the celebrated thermodynamic analogy of black hole mechanics, they are distinguished by having exactly zero temperature. In this talk, I will present a proof showing that extremal black holes can form dynamically from gravitational collapse rather than appearing only as inaccessible limiting objects in parameter space. I will then introduce a series of recently formulated conjectures, together with partial results, that aim to clarify the role of extremal black holes in gravitational collapse, their connection to threshold phenomena, and critical behavior in black hole formation. This talk is based on joint work with Y. Angelopoulos (BIMSA) and R. Unger (UC Berkeley).

I will discuss the phenomenon of collapsing for sequences of Riemannian manifolds whose volume tends to zero while curvature remains uniformly controlled, with particular emphasis on lower Ricci curvature bounds. Understanding the topology and metric structure of the limit spaces, and their relation to the original sequence of manifolds, is a subtle question that has attracted a great deal of attention over the years. I will begin with a brief overview of classical results in the setting of sectional curvature bounds, and then turn to the Ricci framework, including Ricci limit spaces and their synthetic counterparts. In contrast with the sectional curvature setting, collapsing under nonnegative Ricci curvature is much more flexible and can produce wilder limit spaces. I will conclude with a recent joint result with Qin Deng on the topological structure of two-dimensional collapsed limits. Most of the talk will be based on examples.

Get an insight into the research of five new postdoctoral researchers of Mathematics Münster. In short scientific presentations they will introduce their topics.
After the talks, there will be the opportunity to exchange ideas while enjoying tea, coffee and cake in the Common Room.

• Catrin Mair, Homotopy theory in a condensed world
• Stefan Schrott, Optimal transport of stochastic processes
• Mathias Sonnleitner, Connecting and separating dots
• Ferdinand Wagner, Habiro Cohomology & Refined THH
• Alexander Van Werde, On the spectral determinacy of random graphs