Mittwoch      27.09.2023

10:15 Uhr     IA 1/135

Dr. Valdemar Tsanov (Bulgarian Academy of Sciences), "Mackey Lie algebras and universal tensor categories"

Abstract:
A known source of problems in infinite dimensional linear algebra is the fact that the dual space V* to an infinite dimensional vector space V has dimension (the cardinality of a basis) strictly larger than that of V. A recently defined class of algebras - Mackey Lie algebras, or the related Mackey groups - offer a way to study V* and discover some interesting structures. In this talk, based on joint work with Ivan Penkov, I will define Mackey Lie algebras and explain the classification of their ideals, simple tensor modules, and a generalization of Schur-Weyl duality. I will also describe a category of Mackey modules with a universality property similar to the universality property of a tensor product.

Mittwoch      20.09.2023

10:15 Uhr     IA 1/109

Dr. Valdemar Tsanov (Bulgarian Academy of Sciences), "Partial convex hulls of coadjoint orbits"

Abstract:
The coadjoint orbits of compact Lie groups, equipped with their Kostant-Kirillov-Sourieau Kähler structures, represent models for all simply connected compact homogeneous Kähler manifolds. The integral orbits admit embeddings as projective algebraic varieties corresponding to the irreducible unitary representations of the group. Several representation theoretic concepts are related to properties of the convex hull of the orbit, and to its projections to subalgebras. I will introduce the notion of partial convex hulls in this context and indicate some of its relations to representation theory and invariant theory.

Mittwoch      13.09.2023

10:15 Uhr     IA 1/109

Dr. Valdemar Tsanov (Bulgarian Academy of Sciences), "On the nonconvexity of momentum map images"

Abstract:
A classical theorem of Atiyah asserts that the image of a momentum map for a Hamiltonian action of a connected compact Lie group on a compact Kähler manifold is a convex polytope, whenever the group is abelian. For a nonabelian group, a convex polytope is obtained by intersecting the image with a Weyl chamber, but the entire image may or may not be convex. In this talk, I will discuss some phenomena causing nonconvexity, and derive sufficient conditions for convexity of the entire image. In particular, I will present a structural characterization of the compact connected subgroups of a compact group, for which all coadjoint orbits of the larger group have convex momentum images under the subgroup.
 

Mittwoch    16.08.2023

10.00 Uhr    IA 1/53

PD Dr. Stéphanie Cupit-Foutou, „Eine Verallgemeinerung des Sylvester'schen Trägheitssatzes“

Alle Interessenten sind herzlich eingeladen.

Dienstag      11.07.2023

10:00 Uhr     ID 03/653

10:00 - 11:00 Uhr, Tara Trauthwein: Normal approximation of Poisson functionals via generalized p-Poincaré inequalities

11:30 - 12:30 Uhr, Matthias Linenau: Large components in the subcritical Norros-Reittu model

14:30 - 15:30 Uhr, Benedikt Rednoß: Normal approximation for subgraph counts

Mittwoch      05.07.2023

12:15 Uhr     IA 1/109

Oliver Brammen (RUB), "Intersections between harmonic manifolds and complex geometry"

Abstract:
The aim of this talk is to highlight connections between the study of harmonic manifolds and Grauert tubes and pose some questions arising from this connection. To this end, I will give an introduction to harmonic manifolds and informally present results from R.M Aguilarand M.B. Stenzel about the characteristics of their Grauert tube, in case of their existence. Furthermore, I will discuss questions regarding the isometry group of harmonic manifolds.

Mittwoch 21.06.2023

14.15 Uhr    ID 03/445

Katharina Kormann, „Approximation und Struktur - Numerik schnell und zuverlässig“

Alle Interessenten sind anschliessend zu Kaffee/Tee/Kuchen eingeladen.

Dienstag 20.06.2023

16:15 Uhr     IA 1/181

Filip Broćić (Montreal), "Riemannian distance and symplectic embeddings in cotangent bundle"

Abstract  In the talk, I will define a distance-like function d_W on the zero section N of the cotangent bundle T*N. The function d_W is defined using certain symplectic embeddings from the standard ball to the open neighborhood W of the zero section. Using such a function, one can define a length structure on the zero section. The main result of the talk is that in the case when W is equal to the unit disc-cotangent bundle with respect to some Riemannian metric g, the length structure is equal to the Riemannian length. In the process of explaining the proof I will present some results related to the relative type of Gromov width in T*N, and I will give the proof of the strong Viterbo conjecture for the product of two Lagrangian discs in R^{2n}. In the joint work with Dylan Cant, we were able to give a sharper bound on the relative Gromov width, under some constraints, using bordism classes in the free loop space. We also prove the existence of periodic orbits for a large class of Hamiltonians using the same technic. Time permitting, I will present how to use bordism classes to prove these results.

Freitag 16.06.2023

     IA 01/473

14:30 - 15:30 Jakob Hedicke (Montreal)

15:30 - 16:15 coffee break

16:15 - 17:15 Fabian Ziltener (Utrecht)

Jakob Hedicke:

Title: A causal characterisation of positively elliptic elements in Sp(2n)

Abstract: We will use the unique bi-invariant proper closed convex cone structure on the linear symplectic group to characterise the set of Krein-positively elliptic elements in terms of causality.

In particular we will show that the positively elliptic region is globally hyperbolic.

These results can be applied to study the causal geodesics and the Lorentzian distance of a bi-invariant Lorentz-Finsler metric on Sp(2n) and its universal cover, recently introduced by Abbondandolo, Benedetti and Polterovich.

Fabian Ziltener:

Title: Capacities as a complete symplectic invariant

Abstract: This talk is about joint work with Yann Guggisberg. The main result is that the set of generalized symplectic capacities is a complete invariant for every symplectic category whose objects are of the form $(M,\omega)$, such that $M$ is compact and 1-connected, $\omega$ is exact, and there exists a boundary component of $M$ with negative helicity. This answers a question of Cieliebak, Hofer, Latschev, and Schlenk. It appears to be the first result concerning this question, except for results for manifolds of dimension 2, ellipsoids, and polydiscs in $\mathbb{R}^4$.

If time permits, then I will also present some answers to the following question and problem of Cieliebak, Hofer, Latschev, and Schlenk:

Question: Which symplectic capacities are connectedly target-representable?

Problem: Find a minimal generating set of symplectic capacities.

Donnerstag 15.06.2023

16:15 Uhr    IB 3/73

"Eine topologische Tour durch Datenanalyse und Neurale Netze"

Damian Dadanovic

Dieser Vortrag ist eine Einführung in neurale Netze, mit Fokus auf "Convolutional Neural Networks" (CNNs), und eine Einführung in Topologische Datenanalyse (TDA). Anwendungsbeispiele von TDA sind die Analyse von Bildern bzw. Pixel-patche und die Entwicklung von CNNs für Bilderkennung. Gegebenenfalls auch in diesem Vortrag ist eine Erklärung, welche Rolle die Kleinschen Flasche im Kontext der Bilderkennung spielt.

Dienstag 13.06.2023

16:15 Uhr     IA 1/181

Roman Golovko (Prague), "On non-geometric augmentations of Chekanov-Eliashberg algebras"

Abstract: Legendrian contact homology is a modern invariant of Legendrian submanifolds of contact manifolds defined by Eliashberg–Givental–Hofer and Chekanov, and developed by Ekholm–Etnyre–Sullivan for the case of the standard contact vector space.

It is defined to be the homology of the Chekanov-Eliashberg algebra of a given Legendrian submanifold. This invariant is difficult to compute, and, in order to make it computable, one needs to use augmentations. Some augmentations come from certain geometric objects called exact 

Lagrangian fillings, some do not. We will discuss non-geometric augmentations for high dimensional Legendrian submanifolds. Along the way, we prove a Künneth formula for (linearized) Legendrian contact homology for high spuns of Legendrian submanifolds. If time permits, we will also discuss whether algebraic torsion appears in Legendrian contact homology.

Dienstag 13.06.2023

17:30 Uhr     IA 1/181

Sayani Bera (IACS, Calcutta) ), "On non-autonomous attracting basins"

Abstract: The goal of this talk is to discuss briefly the idea of the proof of the Bedford's conjecture (formulated by Fornæss-Stensønes in 2004), on uniform non-autonomous attracting basins of automorphisms of C^k, k \ge 2 and Fatou-Bieberbach domains.

Thus we also affirmatively answer Bedford's question (2000) on uniformizations of the stable manifolds, corresponding to a hyperbolic compact invariant subset of a complex manifold. 

This is a joint work with Dr. Kaushal Verma.

Mittwoch      24.05.2023

13:00 Uhr     ID 03/445

Dr. Martin Kroll, „Der χ^2-Anpassungstext"

Mittwoch      17.05.2023

12:15 Uhr     IB 01/103

Alle Professorinnen, Mitarbeiterinnen und Studentinnen der Fakultät für Mathematik sind herzlich zur Frauenvollversammlung eingeladen.

Tagesordnung: Nachwahl dezentrale Gleichstellungsbeauftragte, siehe Wahlordnung hierzu:
https://www.chancengleich.ruhr-uni-bochum.de/cg/chancen/dezentral.html.de

Donnerstag 11.05.2023

14:15 Uhr     IA 01/177

Stefano Baranzini (Turin), "Morse Index Theorems for Graphs"

Abstract: The classical N-centre problem of Celestial Mechanics describes the behaviour of a point particle under the attraction of a finite number of motionless bodies. Considered as a limit case of a (N+1)-body problem, it has been the object of several results concerning integrability, investigation of chaos and existence of periodic orbits, mostly when the motion is constrained to the Euclidean plane. In particular, variational approaches are convincing in this situation and have produced classes of collision-less periodic solutions, after imposing topological constraints of different natures. Looking for genuine solutions of second order differential equations, the most delicate step resides in avoiding collisions with the centres. Picturing a more realistic situation, a natural extension of these results could be the one in which the motion is constrained to a prescribed Riemannian surface. In this talk we state the N-centre problem on orientable surfaces and we show how it is possible to use variational arguments in order to produce collision-less periodic solutions. Such trajectories will be found among homotopy classes of loops, and their variational and topological properties will be described. This is a joint work with Stefano Baranzini.

Mittwoch      10.05.2023

14:15 Uhr     ID 03/445

Dr. Martin Kroll, „Approximation positiv definiter Funktionen auf kompakten Gruppen“

Dienstag      09.05.2023

16:15 Uhr     IA 01/181

Gian Marco Canneori (Turin), "The N-centre problem on Riemannian surfaces: a variational approach"

Abstract: The classical N-centre problem of Celestial Mechanics describes the behaviour of a point particle under the attraction of a finite number of motionless bodies. Considered as a limit case of a (N+1)-body problem, it has been the object of several results concerning integrability, investigation of chaos and existence of periodic orbits, mostly when the motion is constrained to the Euclidean plane. In particular, variational approaches are convincing in this situation and have produced classes of collision-less periodic solutions, after imposing topological constraints of different natures. Looking for genuine solutions of second order differential equations, the most delicate step resides in avoiding collisions with the centres. Picturing a more realistic situation, a natural extension of these results could be the one in which the motion is constrained to a prescribed Riemannian surface. In this talk we state the N-centre problem on orientable surfaces and we show how it is possible to use variational arguments in order to produce collision-less periodic solutions. Such trajectories will be found among homotopy classes of loops, and their variational and topological properties will be described. This is a joint work with Stefano Baranzini.

Mittwoch      03.05.2023

14:15 Uhr     IA 02/445

14:15 Uhr, Prof. Dr. Kai Zehmisch, „Komplexe Suche nach reellen Lösungen“

15:15 Uhr, Kaffeepause, IA 02/480/481

16:00 Uhr, Prof. Dr. Patrick Henning, „Mehrskalenprobleme und deren numerische Behandlung“