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Sommersemester 2016
20.04.2016 um 17:15 Uhr in Raum 69/125
Prof. Dr. Arne Østvær (Universität Oslo)
Motivic Hopf Equations
The Hopf fibration, introduced by Heinz Hopf in 1931, exhibits a remarkable map from the 3-sphere to the 2-sphere. It was a landmark discovery in topology with many fundamental implications in algebra and topology. In the talk we discuss Hopf maps and their significance, both motivically and topologically.
27.04.2016 um 17:15 Uhr in Raum 69/125
Prof. Dr. Benjamin Nill (Universität Magdeburg)
What's up in Ehrhart Theory of Lattice Polytopes?
A lattice polytope is a polytope whose vertices have integer coordinates. More than fifty years ago Ehrhart proved that counting lattice points in dilates of lattice polytopes is a polynomial function. Since then the study of Ehrhart polynomials has grown into a very active field of research at the crossroad of geometry of numbers, enumerative combinatorics, and toric geometry. The goal of this talk is to present a brand-new result in this area. Along the way, we will learn about the necessary background and basic results, motivation from algebraic geometry and commutative algebra, and open questions.
04.05.2016 um 17:15 Uhr in Raum 69/125
Prof. Dr. Horst Malchow (Universität Osnabrück)
Mathematical and Computational Modelling of Population Dynamics
The dynamics of spatial and spatiotemporal pattern formation in nonlinear biosystems far from equilibrium is of ongoing interest and many mechanisms of structure generation are not known yet. The main aim of modelling biological population dynamics is to improve the understanding of the functioning of food chains and webs as well as their dependence on internal and external conditions. Hence, mathematical models of biological population dynamics have not only to account for growth and interactions but also for spatiotemporal processes like random or directed and joint or relative motion of species, as well as the variability of the environment. Early attempts began with physico-chemical diffusion, exponential growth and Lotka-Volterra type interactions. These approaches have been continuously refined to more realistic descriptions of the development of natural populations. The aim of this talk is to give an extensive introduction to the subject. The fascinating variety of spatiotemporal patterns in such systems and the governing mechanisms of their generation and further dynamics are decribed and related to plankton.
11.05.2016 um 17:15 Uhr in Raum 69/125
Prof. Dr. Christoph Thäle (Universität Bochum)
Random Riemann Surfaces and the Chen-Stein Method
18.05.2016 um 17:15 Uhr in Raum 69/125
Prof. Dr. André Uschmajew (Universität Bonn)
Low Rank Tensor Approximation
Low-rank tensor approximation is an established tool in signal processing and data analysis to decompose multilinear data beyond standard matrix principal component analysis. A different motivation for the development of low-rank tensor techniques comes from the "curse of dimensionality” after discretization of high-dimensional functions as they may arise in scientific computing. Traditional numerical methods for solving (partial) differential, integral, or eigenvalue equations that are based on uniform discretization are severely limited in their application to problems with many variables due to the huge size of the resulting discrete system. Numerical tensor calculus circumvents this problem by representing all involved quantities in data sparse low-rank tensor formats. The variety of available low-rank tenor formats stems from the fact that there is no unique way to generalize the concept of rank from matrices to tensors. In this talk we give a basic introduction to the concepts of rank and low-rank representation of tensors, and their potential application in scientific computing.
25.05.2016 um 17:15 Uhr in Raum 69/125
Dr. Manfred Stelzer (Universität Osnabrück)
Wissenschaftlicher Vortrag im Habilitationsverfahren
Die Dichotomie - elliptisch-hyperbolisch - in der Topologie und anderswo
Wir studieren die Dichotomie elliptisch-hyperbolisch in der Homotopie Theorie und in der Riemannschen Geometrie. Resultate und Vermutungen, diese Dichotomie betrefffend, werden einander gegenübergestellt.
01.06.2016 um 17:15 Uhr in Raum 69/125
Prof. Dr. Rob Stevenson (Universität Amsterdam)
Adaptive Wavelet Methods for Space-Time Variational Formulations of Evolutionary PDEs
Space-time discretization methods require a well-posed space-time variational formulation. Such formulations are well-known for parabolic problems. The (Navier)-Stokes equations can be viewed as a parabolic problem for the divergence-free velocities. Yet to avoid the cumbersome construction of divergence-free trial spaces, we present well-posed variational formulations for the saddle-point problem involving g the pair of velocities and pressure. We discuss adaptive wavelet methods for the optimal adaptive solution of simultaneous space-time variational formulations of evolutionary PDEs. Thanks to use of tensor products of temporal and spatial wavelets, the whole time evolution problem can be solved at a complexity of solving one instance of the corresponding stationary problem.
07.06.2016 um 16:15 Uhr in Raum 69/125
Prof. Dr. Uwe Nagel (University of Kentucky)
Unexpected Curves and Line Arrangements
Given a finite set of points, we consider the following interpolation problem: How many, if any, independent polynomials of a fixed degree vanish at each of the given points with some prescribed multiplicity. This is known for points on a line, but open even for points in a plane. We are particularly interested in situations, where the number of such polynomials is greater than the expected number, as suggested by a naive dimension count. We give criteria for the occurrence of such unexpected curves in a special case which connects to properties of arrangements of lines. In particular, this leads to a new criterion for Terao's conjecture on the freeness of line arrangements. This conjecture posits that freeness of a line arrangement depends only on intersections of the lines, that is, freeness is a combinatorial property of a line arrangement.
15.06.2016 um 17:15 Uhr in Raum 69/125
Prof. Dr. Martin Henk (Technische Universität Berlin)
Discrete Slicing Problems
The well-known (and still open) slicing problem in Convex Geometry, asks whether there exists an absolute constant $c$ so that for every origin-symmetric convex body $K$ of volume 1 there is a hyperplane section of $K$ whose $(n − 1)$-dimensional volume is greater than $c$.
Motivated by a question of Alexander Koldobsky, we are studying a similar slicing problem (and related problems) when the volume functional is replaced by the lattice point enumerator.
22.06.2016 um 17:15 Uhr in Raum 69/125
Prof. Dr. Andreas Eichler (Universität Kassel)
Mathematik zwischen Schule, Hochschule und Schule als schwieriger Weg eines lebenslangen Lernens
Lehrkräfte werden seit einigen Jahren in der mathematikdidaktischen Forschung stärker als diejenigen beachtet, die wesentlich das Geschehen im Mathematikunterricht bestimmen. Wie aber begleitet oder beinflusst man diese Lehrkräfte in Ihrer professionellen Karriere aus der Perspektive der Mathematikdidaktik? In dem Vortrag sollen drei Momente der Begleitung hervorgehoben werden: 1. Das Studium, in dem eine primäre, wenn auch mittelbare Einflussnahme der Mathematikdidaktik auf den Mathematikunterricht stattfindet, 2) die tagtägliche professionelle Tätigkeit, in der die Mathematikdidaktik beschreibend tätig wird und 3) die Fortbildung, in der die Mathematikdidaktik einerseits normativ gestaltet, andererseits empirisch arbeitet. Zu diesen drei Momenten sollen sowohl theoretische Überlegungen, Umsetzungs-Beispiele, wie auch empirische Erkenntnisse diskutiert werden.
