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 15:00 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.
Donnerstag, 4.1.18, 17:00-18:00, Hörsaal II, Albertstr. 23b
Donnerstag, 11.1.18, 17:00-18:00, Hörsaal II, Albertstr. 23b
INVERSE CURVATURE FLOWS AND GEOMETRIC INEQUALITIES
Donnerstag, 18.1.18, 16:00-17:00, Hörsaal II, Albertstr. 23b
In recent years curvature flows have played a crucial role in proving important geometric theorems. For instance, the Ricci flow lead to a proof of the Poincare conjecture, and the inverse mean curvature flow (IMCF) was crucial in the proof of the Riemannian Penrose inequality. In this talk we present further applications of the IMCF. First we review, how classical geometric inequalities, such as the Minkowski inequality for closed convex hypersurfaces, can be generalised to a wider class of hypersurfaces using curvature flows. Secondly, we present new estimates for a Willmore-type energy of hypersurfaces with boundary, satisfying a perpendicular Neumann-type condition on the unit sphere. The crucial ingredient is the IMCF with boundary conditions.
Homologie linearer Gruppen und die Vermutung von Quillen
Donnerstag, 18.1.18, 17:00-18:00, Hörsaal II, Albertstr. 23b
Invariance of closed convex cones for stochastic partial differential equations
Donnerstag, 25.1.18, 17:00-18:00, Hörsaal II, Albertstr. 23b
The goal of this talk is to clarify when a closed convex cone is\ninvariant for a stochastic partial differential equation (SPDE) driven\nby a Wiener process and a Poisson random measure, and to provide\nconditions on the parameters of the SPDE, which are necessary and\nsufficient. As a particular example, we will show how the\nHeath-Jarrow-Morton-Musiela (HJMM) equation from Financial Mathematics,\nwhich models the evolution of interest rate curves, fits into the\npresent SPDE setting. Moreover, we will apply our result about the\ninvariance of closed convex cones in order to investigate when the HJMM\nequation produces nonnegative interest rate curves.