Das Mathematische Kolloquium ist eine gemeinsame wissenschaftliche Veranstaltung des gesamten Mathematischen Instituts. Es steht allen Interessierten offen und richtet sich neben den Mitgliedern und Mitarbeitern des Instituts auch an die Studierenden. Das Kolloquium findet dreimal im Semester am Donnerstag um 17:00 s.t. im Hörsaal II, Albertstr. 23b statt. Danach (gegen 16:15) gibt es Kaffee und Kekse, zu dem der vortragende Gast und alle Besucher eingeladen sind.
Thursday, 18.10.18, 17:00-18:00, Hörsaal II, Albertstr. 23b
Thursday, 8.11.18, 17:00-18:00, Hörsaal II, Albertstr. 23b
How to optimally stir your coffee: Challenges in differential equations
Thursday, 15.11.18, 17:00-18:00, Hörsaal II, Albertstr. 23b
Mixing of different fluids is an ubiquitous phenomenon in sciences, technology, and everyday life. Nevertheless it is fair to say that we are quite far from a clear mathematical understanding of its analytical properties. In this talk I will present my perspective on this problem by describing a suitable mathematical framework for mixing phenomena and by proving a "toy theorem" in a simplified setting. The role of measure theory in the analysis of irregular partial differential equations will be emphasised.
Thursday, 13.12.18, 17:00-18:00, Hörsaal II, Albertstr. 23b
Thursday, 17.1.19, 17:00-18:00, Hörsaal II, Albertstr. 23b
Evolutionary Gamma convergence for gradient systems
Thursday, 24.1.19, 17:00-18:00, Hörsaal II, Albertstr. 23b
Many ordinary and partial differntial equations can be written as a gradient flow, which means that there is an energy functional that drives the evolution of the the solutions by flowing down in the energy landscape. The gradient is given in terms of a dissipation structure, which in the simplest case is a Riemannian metric. We discuss classical and nontrivial new examples in reaction-diffusion systems or friction mechanics. We will emphasize that having a gradient structure for a given differential equation means that we add additional physical information.\n\nConsidering a family of gradient systems depending on a small parameter, it is natural to ask for the limiting (also called effective) gradient system if the parameter tends to 0. This can be achieved on the basis of De Giorgi's Energy-Dissipation Principle (EDP). We discuss the new notion of "EDP convergence" and show by examples that this theory is flexible enough to allow for situations where starting from quadratic dissipation potentials we arrive at physically relevant, effective dissipation potentials that are no\nlonger quadratic, namely exponential laws for transmission at membranes or slip-stick motion on rough surfaces.
Diffusion in strongly layered domains
Thursday, 31.1.19, 17:00-18:00, Hörsaal II, Albertstr. 23b
Inspired by chemical signalling in cell organelles\nwe analyse the effect of strongly layered domains\non diffusion. Homogenisation\nreveals memory effects and splitting into PDE-ODE systems, i.e. the specific geometry of\nthe domain has strong qualitative effects on\nthe solution of the heat equation. We will discuss these results\nin context with phenomena observed in cell biology.
Thursday, 7.2.19, 17:00-18:00, Hörsaal II, Albertstr. 23b