Veranstaltungsübersicht -- Wintersemester 2019/2020

Montag,
2019-10-28
16:15 Uhr
Raum 404, Ernst-Zermelo-Str. 1
Ida Zadeh (ICTP): Lifting BPS States on K3 and Mathieu Moonshine

The elliptic genus of K3 is an index for the 1/4-BPS states of its sigma-model. At the torus orbifold point there is an accidental degeneracy of such states. We blow up the orbifold fixed points and show that this fully lifts the accidental degeneracy of the 1/4-BPS states with dimension h=1. Thus, at a generic point near the Kummer surface the elliptic genus measures not just their index, but counts the actual number of these BPS states. Finally, we comment on the implication of this for symmetry surfing and Mathieu moonshine.

Montag,
2019-11-04
16:15 Uhr
Raum 404, Ernst-Zermelo-Str. 1
Severin Barmeier: Deformations of path algebras of quivers with relations from a geometric perspective

Path algebras of quivers with relations naturally appear in algebraic geometry as endomorphism algebras of so-called tilting bundles. In this setting, deformations of such quotients of path algebras can be used to give a concrete description of deformations of the category of (quasi)coherent sheaves as Abelian category, which are known to combine both "classical" deformations of the variety and "noncommutative" algebraic deformation quantizations.

In this talk I will present recent joint work with Zhengfang Wang for describing deformations of path algebras of quivers with relations algebraically / combinatorially. I plan on focussing on examples of geometric origin and will try to explain such deformations from a geometric perspective.

Montag,
2019-11-11
16:15 Uhr
Raum 404, Ernst-Zermelo-Str. 1
Ksenia Fedosova: A (possible) regularization of the Selberg zeta function

Selberg zeta functions are zeta functions associated with the geodesic flow on a hyperbolic surface and, sometimes, a representation of the fundamental group of the surface. The spectral theory of the Selberg zeta for unitary representations is well-known, but, however, for certain no-unitary representations the Selberg zeta function may even not exist.

In the talk, I would like to suggest a way of the regularization of the Selberg zeta function to such types of non-unitary representations using the transfer operator approach.

Montag,
2019-11-18
16:00-17:00 Uhr
Raum 404, Ernst-Zermelo-Str. 1
Jonas Schnitzer: Poisson geometry and beyond

Poisson brackets appear in different fields of mathematics and physics, such as the theory of Lie algebras and classical mechanics. This talk is meant to give a short introduction to the subject of Poisson geometry in general and, afterwards, to discuss the connection of Poisson structures and Lie groupoids/algebroids, symplectic geometry and deformation quantization.

Montag,
2019-11-18
17:00-18:00 Uhr
Raum 404, Ernst-Zermelo-Str. 1
Andriy Haydys: On the blow up set for the Seiberg-Witten equations with two spinors
Montag,
2019-11-25
16:15 Uhr
Raum 404, Ernst-Zermelo-Str. 1
Vera Gahlen: Quaternionic Line Bundles

In contrast to real and complex line bundles, quaternionic line bundles are not classified by a suitable characteristic class. However, there are results on the classification over four and five dimensional spin manifolds.

This talk is an introduction to quaternionic line bundles and their classification. We will see why the approach to classification in the real and complex cases does not transfer to the quaternionic setting. Based on this, I would like to present different approaches to the classification over spin manifolds of low dimension.

Montag,
2019-12-02
16:15 Uhr
Raum 404, Ernst-Zermelo-Str. 1
Marius Amann: Singularity Theorems over Averages on globally hyperbolic Spacetimes
Freitag,
2019-12-06
10:15-11:45 Uhr
Raum 318, Ernst-Zermelo-Str. 1
Clara Aldana (Barranquilla, Colombia): Maximal determinants of Schrödinger operators on finite intervals

In this talk I will present the problem of finding extremal potentials for the functional determinant of a one-dimensional Schrödinger operator defined on a bounded interval with Dirichlet boundary conditions. We consider potentials in a fixed $L^q$ space with $q\geq 1$. Functional determinants of Sturm-Liouville operators with smooth potentials or with potentials with prescribed singularities have been widely studied, I will present a short review of these results and will explain how to extend the definition of the functional determinant to potentials in $L^q$. The maximization problem turns out to be equivalent to a problem in optimal control. I will explain how we obtain existence and uniqueness of the maximizers. The results presented in the talk are join work with J-B. Caillau (UCDA, CNRS, Inria, LJAD) and P. Freitas (Lisboa).

Montag,
2019-12-09
16:15 Uhr
Raum 404, Ernst-Zermelo-Str. 1
Yaël Frégier (Lens): tba

tba

Montag,
2019-12-16
16:15 Uhr
Raum 404, Ernst-Zermelo-Str. 1
Léo Bénard (Göttingen): Asymptotic of twisted Alexander polynomials and hyperbolic volume

Given a hyperbolic 3-manifold M of finite volume, we study a family of twisted Alexander polynomials of M. We show an asymptotic formula for the behavior of those polynomials on the unit circle, and recover the hyperbolic volume as the limit. It extends previous works of Müller (for M closed) and Menal-Ferrer--Porti. This is a joint work with Jerome Dubois, Michael Heusener (Clermont-Ferrand) and Joan Porti (Barcelona).

Montag,
2020-01-13
16:15 Uhr
Raum 404, Ernst-Zermelo-Str. 1
Aeran Fleming (Liverpool): Explicit Kähler packings of projective complex manifolds

In this talk I will start by introducing the concept of multipoint Seshadri constants and discuss their relationship with Nagata's conjecture on plane curves. I will then introduce the notion of a Kähler packing and show that there is a direct connection between the multipoint Seshardi constant and the existence of Kähler packings. To end I will provide an example of a Kähler packing of a toric variety which highlights a connection between Kähler packings of certain polytopes and their corresponding varieties.

Montag,
2020-01-20
16:15 Uhr
Raum 404, Ernst-Zermelo-Str. 1
Karina Stelter (Freiburg): The Euler characteristic - an invariant with many incarnations

The Euler characteristic plays a major role as a topological invariant, for example in Euler's polyhedron theorem. It can also be understood as an analytic invariant. The Poincaré-Hopf-Index theorem builds a bridge between these two realms. Furthermore, it is a geometric invariant as in the theorem of Gauß-Bonnet.

In this talk, I will focus on homologies and explain the relation between the Euler characteristic and the so-called Betti numbers, which are the rank of the homology groups of an underlying complex. The Euler characteristic is therefore also an invariant of algebraic objects.

Montag,
2020-01-27
16:15 Uhr
Raum 404, Ernst-Zermelo-Str. 1
Jonas Lenthe: Steenrod squares in differential cohomology
Montag,
2020-02-03
16:15 Uhr
Raum 404, Ernst-Zermelo-Str. 1
Lukas Hoffmann (Freiburg): TBA
Dienstag,
2020-02-04
16:15 Uhr
Fakultätssitzungsraum (4.OG)
Fabricio Valencia: Invariant generalized geometry on maximal flag manifolds

The purpose of this talk is to describe the set of generalized complex structures on a maximal flag manifold which are invariant by the adjoint action on the flag, as well as study some of their geometric properties. We will give an explicit expression for the invariant pure spinor line associted with each of these structures. We will characterize all invariant generalized Kähler structures on a maximal flag manifold. Finally, we will describe the quotient spaces determined by the set of all invariant generalized complex (resp. almost Kähler) structures under the action by invariant B-transformations. This is a joint work with Elizabeth Gasparim and Carlos Varea.

Montag,
2020-02-10
16:15 Uhr
Raum 404, Ernst-Zermelo-Str. 1
Paul Wabnitz (Bremen): tba

tba

Dienstag,
2020-02-25
14:15 Uhr
Raum 404, Ernst-Zermelo-Str. 1
Elizabeth Gasparim (Antofagasta, Chile): TBA

Abonnieren

Die Einträge dieser Veranstaltung können im iCalender Format abonniert werden. die URL dazu lautet:
http://wochenprogramm.mathematik.uni-freiburg.de/ical/WS2019-2020/OS-DiffGeo.ics