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Winter term 2015/16

03. February 2016

Katja Polotzek (Technische Universität Dresden)

Numerical computation of rotations sets of torus homeomorphisms

The abstract can be found here.

27. January 2016

Siegfried Beckus (Friedrich-Schiller-Universität Jena)

Spectral Approximation of Schrödinger Operators: Continuous Behavior of the Spectra

The abstract can be found here.

20. January 2016

Frederik Witt (Universität Stuttgart)

Holomorphe integrable Systeme, Prymvarietäten und Hyperkählermetriken

Hitchins Higgs-Modulraum ist ein zentrales Beispiel für ein holomorph integrables System (HIS), dem komplexen Gegenstück integrabler Systeme aus der klassischen Mechanik. Insbesondere fasern HIS in komplexe Tori, für den Higgs-Modulraum beispielsweise in sogenannte Prymvarietäten. Darüber hinaus existieren auf HIS Hyperkählermetriken, eine spezielle Klasse Ricci-flacher Riemannscher Metriken. In diesem Vortag möchte ich zunächst Hitchins Konstruktion und Geometrie des Higgs-Modulraum eingehend diskutieren, bevor ich neuere Ergebnisse zur Asymptotik der Geometrie anspreche, die auf gemeinsamer Arbeit mit R. Mazzeo, J, Swoboda und H. Weiß beruhen.

06. January 2016

Mickaël Kourganoff (École normale supérieure de Lyon)

Similarity structures and De Rham decomposition

16. December 2015

Jun Masumune (Friedrich-Schiller-Universität Jena)

On the Liouville property of harmonic functions under certain integrable conditions

09. December 2015

Christian Oertel (Friedrich-Schiller-Universität Jena)

Model sets with positive entropy

25. November 2015

Markus Lange (Friedrich-Schiller-Universität Jena)

On Asymptotic Expansions for Spin Boson Models

18. November 2015

Alexey Glutzuk (CNRS, ENS de Lyon and Higher School of Economics, Moscow)

On periodic orbits in complex planar billiards

A conjecture of Victor Ivrii (1980) says that in every billiard with smooth boundary the set of periodic orbits has measure zero. This conjecture is closely related to  spectral theory. Its particular case for triangular orbits was proved by M. Rychlik (1989, in two dimensions), Ya. Vorobets (1994, in any dimension) and other mathematicians. The case of quadrilateral orbits in dimension two was treated in our joint work with Yu. Kudryashov (2012). We study the complexified version of planar Ivrii's conjecture with reflections from a collection of planar holomorphic curves. We present the classification of complex counterexamples with four reflections and partial positive results. The recent one says that a billiard on one irreducible complex algebraic curve without too complicated singularities cannot have a two-dimensional family of periodic orbits of any period. The above complex results have applications to other problems on real billiards: Tabachnikov's commuting billiard problem and Plakhov's invisibility conjecture.

11. November 2015

Tobias Oertel-Jäger (Friedrich-Schiller-Universität Jena)

Model sets and Toeplitz flows

04. November 2015

Alexander Lyapin (Siberian Federal University)

The Mouivre theorem for multidimensional linear difference equations

28. October 2015

Boris Kruglikov (Universitetet i Tromsø)

On the first gap in symmetry dimensions

I will present an interesting geometric phenomenon: often in finite-type systems there is a gap in dimensions between the most symmetric model and the other (non-flat) ones. I will give some general results and then illustrate this for a variety of geometries. Among the latest advances I will discuss the submaximal symmetric structures in c-projective geometry (joint with Vladimir Matveev and Dennis The) and nearly pseudo-Kähler geometry (joint with Henrik Winther) and CR-geometry.

Antoine Gournay (Technische Universität Dresden)

Lp cohomology, random walks and boundary values

27. October 2015

Henrik Winther (Universitetet i Tromsø)

Strictly nearly pseudo-Kähler manifolds with large symmetry groups

We consider strictly nearly pseudo-Kähler manifolds of dimension 6 and a closely related generalization of these called non-degenerate almost complex structures. We explore the relationship between these and use this to determine the maximal, sub-maximal and sub-submaximal symmetry dimension of such spaces and give a complete list of examples realizing these symmetry dimensions (joint work with Boris Kruglikov).