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SS 2016
20.04.2016 at 5:15 p.m. in room 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 at 5:15 p.m in room 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 at 5:15 p.m. in room 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 at 5:15 p.m. in room 69/125
Prof. Dr. Christoph Thäle (Universität Bochum)
Random Riemann Surfaces and the Chen-Stein Method
18.05.2016 at 5:15 p.m. in room 69/125
Prof. Dr. André Uschmajew (Universität Bonn)
Low Rank Tensor Approximation
25.05.2016 at 5:15 p.m. in room 69/125
Dr. Manfred Stelzer (Universität Osnabrück)
Habilitation Lecture
01.06.2016 at 5:15 p.m. in room 69/125
Prof. Dr. Rob Stevenson (University of Amsterdam)
Adaptive Wavelet Methods for Space-Time Variational Formulations of Evolutionary PDEs
07.06.2016 at 4:15 p.m. in room 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.
