Das Institutskolloquium findet während der Vorlesungszeit an jedem Donnerstag um 17:15 Uhr im Raum 05-432 (Hilbertraum) statt. Ab 16:45 Uhr gibt es Kaffee und Kuchen.
Programm
04.05.2017 16 Uhr c.t. Festkolloquium aus Anlass der Geburtstage von Prof. Dr. Heinrich Mülthei und Prof. Dr. Claus Schneider
Prof. Dr. Ansgar Jüngel (TU Wien)
Nanoprozessoren: unvorstellbar klein und unglaublich schnell. Modellhierarchie, Analysis, Simulationen
Dr. Jochen Göttelmann (Lufthansa Cargo)
Von Wavelets, Portlets und Winglets
18.05.2017 17 Uhr c.t. JunProf. Dr. Andrea Barth (Universität Stuttgart)
Quantification of Uncertainty via Multilevel Monte Carlo Methods
01.06.2017 17 Uhr c.t. Prof. Dr. Lutz Hille (Universität Münster)
Inverse Limits of moduli spaces of quiver representations.
22.06.2017 17 Uhr c.t. Prof. Dr. Leonid Mytnik (Technion Haifa, Israel)
Regularity properties of super-Brownian motion.
29.06.2017 17 Uhr c.t. Prof. Dr. Tom Archibald (Simon Fraser University, Burnaby, Kanada)
Definition, Theorem, Proof: Shifting mathematical practice in measure theory to 1950.
06.07.2017 17 Uhr c.t. PD Dr. Matthias Schneider (Universität Mainz)
Geschlossene magnetische Geodäten
13.07.2017 17 Uhr c.t. Name
Titel
Abstracts:
04.05.2017: Prof. Dr. Ansgar Jüngel (TU Wien)
Der Erfolg der Computertechnologie basiert wesentlich auf der Miniaturisierung der Halbleiterbauteile in den Computerprozessoren. Moderne Bauteile haben einen Durchmesser von nur wenigen Nanometern, so dass aufgrund physikalischer Grenzen die Entwicklung neuer Technologien notwenig wird. In diesem Vortrag werden einige Aspekte der mathematischen Modellierung von Halbleiterbauelementen, der Analysis der resultierenden partiellen Differentialgleichungen und ihre numerische Simulation mit Hilfe von Finiten Elementen oder Finiten Volumen vorgestellt. Der Fokus liegt auf kinetischen Gleichungen und ihre Diffusionsgrenzgleichungen. Für deren Analysis wird eine neue Technik (systematische partielle Integration) erlaeutert, die auf polynomielle Entscheidungsprobleme der reellen algebraischen Geometrie führt.
18.05.2017: JunProf. Dr. Andrea Barth (Universität Stuttgart)
Multilevel Monte Carlo methods were introduced to decrease the computational complexity of the calculation of, for instance, the expectation of a random quantity. More precisely, in comparison to standard Monte Carlo methods, the computational complexity is (asymptotically) equal to the calculation of one sample of the problem on the finest discretization grid used. The price to pay for this increase in efficiency is that the problem must be solved not only on one (fine) grid, but on a hierarchy of discretizations. This implies, first, that the solution has to be represented on all grids and, second, that the variance of the detail (the difference of approximate solutions on two consecutive grids) converges with the refinement of the grid.
In this talk, I will give an introduction to multilevel Monte Carlo methods in the case when the variance of the detail does not converge uniformly. The idea is illustrated by the calculation of the expectation for an elliptic problem with a random (multiscale) coefficient and then extended to approximations of discontinous nature, e.g. Poisson noise.
01.06.2017: Prof. Dr. Lutz Hille (Universität Münster)
Moduli spaces of quiver representations are a class of basic GIT-quotients. The construction by King depends on a choice of a linearization, this choice is in most cases far from being natural. To avoid this problem, we consider in a joint work with Mark Blume the inverse limit of those moduli spaces over all linearizations.
The principal aim of this talk is to compute this inverse limit in several instances and to obtain, for very simple quivers with small dimension vectors, well-known moduli spaces, like the Losev-Manin moduli space of chains of rational curves and the Mumford-Knudson moduli space of rational curves with marked points.
Thus it is desirable to compute these inverse limits in other instances, where we have partial results.
22.06.2017: Prof. Dr. Leonid Mytnik (Technion Haifa, Israel)
We consider super-Brownian motion — measure-valued process that can be constructed as a limit of critical branching Brownian motions. It has been wellknown for a long time that the super-Brownian motion with quadratic branching mechanism has a density provided that the spatial dimension d equals to one. However some fine properties of the densities were not well understood. We study the boundary of the zero set of the density of super-Brownian motion.
We also show how some regularity properties of the super-Brownian motion could be determined via properties of the so-called log-Laplace equation.
Part of this talk is based on a joint work with C. Mueller and E. Perkins.
29.06.2017: Prof. Dr. Tom Archibald (Simon Fraser University, Burnaby, Kanada)
The way of presenting mathematics, whether as research or in lecture courses, that was completely standard by the mid-twentieth century, and which remains usual, developed in the first half of that century from nineteenth-century roots. We take as our starting point a debate on how best to present measure theory circa 1950, with Paul Halmos on one side and Jean Dieudonné on the other. The points of disagreement notably include the relationship between a theory and its most important mathematical uses; and the criteria for choice of definitions. In this paper we examine different positions on these matters in the earlier history of measure theory, taking examples from work of Carathéodory, Nikodym, and others. The aim of this work in progress is to arrive at a more nuance historical understanding of the competing values at work in the development of the standard mathematical practice of the mid to late twentieth century.
06.07.2017: PD Dr. Matthias Schneider (Universität Mainz)
Magnetische Geodäten sind Bahnen von geladenen Teilchen in einem Magnetfeld. Von besonderem Interesse sind periodische Bahnen. In diesem Vortrag werden Existenzresultate für geschlossene magnetische Geodäten auf Flächen vorgestellt und diskutiert.
Archiv: