Summer term 2017
6. April 2017
14:30 (A&G), seminar room 3517
Boris Doubrov (Belarussian State University, Minsk)
Real hypersurfaces in C3 with large symmetry
16:00 (DS&MP), seminar room 3517
Tobias Weich (Universität Paderborn)
Ruelle Resonanzen
In a first part of the talk we introduce the notion of Ruelle resonances for dynamical systems and their implications for the decay of correlations. We will in particular focus on the modern spectral theoretical approach and explain how Ruelle resonances are related to poles of meromorphically continued resolvents. In the rest of the talk we will present two recent results on the support of the resonant states and the Ruelle spectrum on locally symmetric spcaes.
26. April 2017
15:00 (A&G), seminar room 3319
Alexey Bolsinov (Loughborough University)
Projectively equivalent metrics in small dimensions
27. April 2017
16:00 Mathematical Colloquium Jena, CZ3, SR 308 - FÄLLT wegen Krankheit AUS!
Andreas Hamel (Free University of Bozen)
An abstract convexity approach to set relations and set optimization
11. May 2017
14:30 (A&G), seminar room 3517
Siegfried Beckus (Israel Institute of Technology)
The space of Delone dynamical systems and related objects
Recent developments show that the space of dynamical systems equipped with the Chabauty-Fell topology plays an important role in the spectral theory of Schrödinger operators as it greatly encodes topological and dynamical properties. Specifically, it is shown that the spectra of these operators behave continuous in the Hausdorff metric if and only if the underlying dynamical systems vary continuously in the Chabauty-Fell topology. This raises further questions whether other related quantities behave well in this topology. During the talk, we focus on the space of Delone dynamical systems in a locally compact, second countable Hausdorff group G acting by translation. Under the additional assumption of unique ergodicity of the limit point, the weak-* convergence of corresponding invariant probability measures on these Delone dynamical systems is proven.
Delone sets model solids in mathematical physics while associated Schrödinger operators describe the long time behavior of an particle in such a solid. Using the previously developed theory, we show that also other spectral quantities of these operators behave well in the Chabauty-Fell topology.
16:00 (DS&MP), seminar room 3517
Martin Tautenhahn (TU Chemnitz)
Quantitative unique continuation and application to control theory for the heat equation
18. May 2017
14:30 (A&G), seminar room 3517
Zhiyuan Zhang (Université Paris Diderot)
Density of mode-locking for a class of skew-products
16:30 Mathematical Colloquium Jena, CZ3, SR 317
Matthias Kreck (Universität Bonn)
Ein übersehenes Problem: Bettizahlen geschlossener Mannigfaltigkeiten
01. June 2017
16:00 (DS&MP), seminar room 3517
Felix Krahmer (Technische Universität München)
On the connection between analog and digital conversion and the roots of Chebyshev polynomials
Sigma-Delta modulation is a popular approach for coarse quantization of audio signals. That is, rather than taking a minimal amount of samples and representing them with high resolution, one considers redundant representations and works with a low resolution. The underlying idea is to employ a feedback loop, incorporating the prior evolution of the sampling error. In this way, the representation of a sample can partially compensate for errors made in previous steps. The design of the filter at the core of the feedback loop is crucial for stability and hence for performance guarantees. Building on work of Güntürk (2003) who proposed to use sparse filters, we optimize the sparsity pattern, showing that a distribution mimicking the roots of Chebyshev polynomials of the second kind is optimal. The focus of this talk will be on the interplay between complex variables, orthogonal polynomials, and signal processing in the proof. This is joint work with Percy Deift and Sinan Güntürk (Courant Institute of Mathematical Sciences, NYU).
8. June 2017
16:00 Mathematical Colloquium Jena, CZ3, SR 308
Erich Wittmann (TU Dortmund)
Was läuft im Mathmatikunterricht und in der Lehrerbildung falsch? Wie könnte umgesteuert werden?
15. June 2017
16:00 (DS&MP), SR 131 CZ
Pablo Ramacher (Marburg)
Equivariant convex and subconvex bounds for eigenfunctions and Hecke-Maas forms
22. June 2017
14:30 (A&G), seminar room 3517
Moussa Ndour (TU Dresden)
Qualitative changes in flow patterns
We discuss a global approach for detecting early-warning signals for qualitative changes in flow patterns. As examples, we consider the double gyre and 4-mode quasi-geostrophic circulation models.
16:00 (DS&MP), seminar room 3517
Maximilian Engel (Imperial College London)
Quasi-stationary dynamics and bifurcations of random dynamical systems
We look at Markov processes that induce a random dynamical system evolving in a domain with forbidden states constituting a trap. The process is said to be killed when it hits the trap and it is assumed that this happens almost surely. We investigate the behavior of the process before being killed, asking what happens when one conditions the process to survive for a long time.
The topic goes back to the pioneering work by Yaglom in 1947 but in recent years new ideas have been developed. We discuss concepts like quasi-stationary and quasi-ergodic distributions, calling the associated random dynamics quasi-stationary or quasi-ergodic if such distributions exist. Given their existence, we can define average Lyapunov exponents and the Dichotomy spectrum of the random dynamical system with killing and describe the bifurcation behavior of typical examples of stochastic bifurcation theory within this environment. The underlying philosophy is to exhibit the local character of random bifurcations for stochastic differential equations which are usually hidden in the global analysis. We further relate these concepts to dynamical systems with holes.
29. June 2017
16:00 Mathematical Colloquium Jena, CZ3, SR 309
Arno Berger (University of Alberta)
Digits and dynamics - A tour of Benford's Law
Benford's Law (BL), a notorious gem of mathematics folklore, asserts that leading digits of numerical data are usually not equidistributed, as might be expected, but rather follow one particular logarithmic distribution. Since first recorded by Newcomb in 1881, this apparently counter-intuitive phenomenon has attracted much interest from scientists and mathematicians. This talk will introduce and discuss some of the intriguing aspects of BL, and relate them to problems in probability and number theory and, above all, dynamics.
In view of their pivotal role as models of many real-world processes, it is natural to ask whether dynamical systems can actually comply with BL in some sense or other and, if so, whether in turn something about dynamics can be learned from this. The talk will answer both questions in the affirmative. Moreover, all real data sets, such as e.g. data recorded from a dynamical system, necessarily are finite, and determining exactly what (and what not) BL means for such data will emerge as a formidable challenge in itself.
06. July 2017
14:30 (A&G), seminar room 3517
Pablo Rodriguez-Sanchez (University of Wageningen)
Invasive species: a mathematician among biologists
16:00 (DS&MP), seminar room 3517
Sara Munday (University of Bologna)
A Birkhoff ergodic theorem for infinite measure systems
The abstract can be found here.