Vorträge in der Woche 20.06.2016 bis 26.06.2016

Dienstag, 21.06.2016: On the hyperbolic conservation laws with randomness: the case for Lévy noise

Imran H. Biswas (Tata Institute of Fundamental Research, Bangalore/Indien)

A large number of physical phenomenon could be mathematically described with the help of hyperbolic conservation laws. The inherent complexities make it only natural to able to account for possible random- ness/noise in the descriptions. In this talk, we will try to make case for Lévy (jump-diffussion) type of noise and contend that it brings us a step closer to reality. We will describe some of the recent advances related existence, uniqueness, stability for stochastic conservation laws that are driven by Lévy noise.

Dienstag, 21.06.2016: The j-function II

Benedikt Otto

Mittwoch, 22.06.2016: Partial Differential Equations in Geometry

Prof. Dr. Simon Brendle (Stanford University und Columbia University)

A central theme in geometry is the study of manifolds and their curvature. In this lecture series, we will discuss how techniques involving partial differential equations have shed light on several longstanding problems in global differential geometry. In particular, we will focus on the geometry of hypersurfaces, and discuss the isoperimetric inequalities, Alexandrov’s theorem on embedded surfaces in R n of constant mean curvature, as well as our proof of Lawson’s 1969 conjecture concerning embedded minimal tori in S 3 . Time permitting, I will discuss some recent results on the classification of self-similar solutions to geometric flows.

Donnerstag, 23.06.2016: Existence of AVTD Solutions to the Einstein Equations in Wave Gauges by Non-Analytic Fuchsian Methods

Dr. Ellery Ames (Chalmers University of Technology)

An asymptotically velocity term dominated (AVTD) solution of the Einstein equations is a non-oscillatory singular solution which at each spatial point asymptotically approaches a Kasner solution near the singularity. The identification of AVTD behavior in symmetry-defined classes of spacetimes has been useful in probing the question of strong cosmic censorship in general relativity. Existence of families of AVTD solutions can be naturally proved as an application of Fuchsian methods for PDE. In this talk I present a class of AVTD solutions with Gowdy symmetry in wave gauges, and also discuss the Fuchsian theorem in the smooth category on which the existence of such solutions based.

Donnerstag, 23.06.2016: On a geometric variational principle for computing slow invariant attracting manifolds in dynamical systems of chemical reaction kinetics

Prof. Dr. Dirk Lebiedz (Universität Ulm)

Differential equation models for chemical reaction kinetics are dissipative dynamical systems, usually sharing high stiffness, multiple time scale character and often also high dimensionality. Modeling the slow modes of kinetics plays a significant role in dimension reduction approaches for such models within reactive flow applications and can be achieved by computing slow invariant attracting manifolds (SIAM) in phase space. A numerically efficient variational approach for the approximation of SIAM will be presented and issues concerning the search for an exact variational principle characterizing the slow manifolds will be discussed.

Donnerstag, 23.06.2016: A mathematical physics perspective on spin wave theory

Dr. Marcin Napiórkowski (IST Austria)

Spin wave theory suggests that low temperature properties of the Heisenberg model can be described in terms of noninteracting quasiparticles called magnons. In my talk I will review the basic concepts and predictions of spin wave approximation and report on recent rigorous results in that direction.