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.
Sonderkolloquium Stochastik
Donnerstag, 5.11.15, 12:30-13:30, Raum 404, Eckerstr. 1
Alle Vorträge finden im Seminarraum 404 in der Eckerstraße 1 statt.\n\n12:30 Uhr Dr. Philipp Harms \nHypoelliptic diffusions in mathematical finance\n\n17:00 Uhr: Dr. Martin Herdegen \nGleichgewichtsmodelle mit kleinen Transaktionskosten
Donnerstag, 5.11.15, 17:00-18:00, Hörsaal II, Albertstr. 23b
Sonderkolloquium Stochastik
Freitag, 6.11.15, 08:00-09:00, Raum 404, Eckerstr. 1
Alle Vorträge finden im Seminarraum 404 in der Eckerstraße 1 statt.\n\n08:00 Uhr: Dr. Jakob Söhl \nStatistik für Levy-Prozesse und Diffusionen\n\n10:00 Uhr: Dr. Joscha Diehl \nMethoden für stochastische partielle Differentialgleichungen
Super-Ricci flows of metric measure spaces
Donnerstag, 12.11.15, 17:00-18:00, Hörsaal II, Albertstr. 23b
A time-dependent family of Riemannian manifolds is a\nsuper-Ricci flow if \(2 Ric + \bpartial_t g \bge 0\).\nThis includes all static manifolds of nonnegative Ricci\ncurvature as well as all solutions to the Ricci flow\nequation.\nWe extend this concept of super-Ricci flows to\ntime-dependent metric measure spaces. In particular, we\npresent characterizations in terms of dynamical convexity\nof the Boltzmann entropy on the Wasserstein space as well\nin terms of Wasserstein contraction bounds and gradient\nestimates. And we prove stability and compactness of\nsuper-Ricci flows under mGH-limits.
Aspherical manifolds, what we know and what we do not know
Donnerstag, 19.11.15, 17:00-18:00, Hörsaal II, Albertstr. 23b
Der Vortrag wird kurzfristig abgesagt!
The Nash problem for arc spaces
Donnerstag, 26.11.15, 17:00-18:00, Hörsaal II, Albertstr. 23b
Algebraic varieties (zeroes of polynomial equations) often present singularities: points around which the variety fails to be a manifold, and where the usual techniques of calculus encounter difficulties. The problem of understanding singularities can be traced to the very\nbeginning of algebraic geometry, and we now have at our disposal many tools for their study. Among these, one of the most successful is what is known as resolution of singularities, a process that transforms (often in an algorithmic way) any variety into a smooth one, using a\nsequence of simple modifications.\n\nIn the 60's Nash proposed a novel approach to the study of\nsingularities: the arc space. These spaces are natural higher-order analogs of tangent spaces; they parametrize germs of curves mapping into the variety. Just as for tangent spaces, arc spaces are easy to understand in the smooth case, but Nash pointed out that their geometric structure becomes very rich in the presence of\nsingularities.\n\nRoughly speaking, the Nash problem explores the connection between the topology of the arc space and the process of resolution of singularities. The mere existence of such a connection has sparked in recent years a high volume of activity in singularity theory, with connections to many other areas, most notably birational geometry and\nthe minimal model program.\n\nThe objective of this talk is to give an overview of the Nash problem. I will give a precise description of the problem, and discuss the most recent developments, including the proof of Fernandez de Bobadilla and\nPe Pereira of the Nash conjecture in dimension two, and our extension of their result to arbitrary dimension.