Veranstaltungsübersicht -- Sommersemester 2024

Montag,
2024-04-22
16:15-18:00 Uhr
Raum 125, Ernst-Zermelo-Str. 1
Prof. Dr. Bernd Ammann (Regensburg): Minimal geodescis

A geodesic $c:\mathbb{R}\to M$ is called minimal if a lift to the universal covering globally minimizes distance. On the $2$-dimensional torus with an arbitrary Riemannian metric there are uncountably many minimal geodesic. In dimension at least $3$, there may be very few minimal geodesics. Let us assume that $M$ is closed. In 1990 Victor Bangert has shown that the number of geometrically distinct minimal geodesics is bounded below by the first Betti number $b_1$.

In joint work with Clara Löh, we improve Bangert's lower bound and we show that this number is at least $b_1^2+2b_1$.

The talk will have many ties to previous research done in Freiburg many years ago: to the research of Victor Bangert, to the Diploma thesis I have written in Freiburg in 1994 in Bangert's group, to the research of the younger Burago, when he was a long term guest in Freiburg and other aspects.

Montag,
2024-04-29
16:15-17:45 Uhr
Raum 125, Ernst-Zermelo-Str. 1
Fabian Kertels: Multiplication of BPS states in heterotic torus theories

The space of states of an N = 2 superconformal field theory contains an infinite-dimensional subspace of Bogomol'nyi–Prasad–Sommerfield (BPS) states, defined as states with minimal energy given their charge. In particular, they arise in worldsheet theories of strings. In this setting, Harvey and Moore introduced a bilinear map on BPS states.

This talk presents a mathematically rigorous approach to this construction, which has been considered promising but not properly understood for almost 30 years now. The example used throughout is that of a heterotic string with all but four dimensions compactified on a torus. For this case, the BPS states were claimed to form a Borcherds–Kac–Moody algebra, as introduced in Borcherds' proof of the monstrous moonshine conjectures.

The first half of the talk, unfortunately, consists in pointing out problems with the proposed construction. The second half will provide more details on selected aspects, such as the existence of a finite-dimensional Lie algebra of massless BPS states.

Montag,
2024-05-27
16:00 Uhr
Raum 125, Ernst-Zermelo-Str. 1
Jonas Schnitzer: Quantization of momentum maps and adapted formality morphisms

If a Lie group acts on a Poisson manifold by Hamiltonian symmetries there is a well-understood way to get rid of unnecessary degrees of freedom and pass to a Poisson manifold of a lower dimension. This procedure is known as Poisson-Hamiltonian reduction. There is a similar construction for invariant star products admitting a quantum momentum map, which leads to a deformation quantization of the Poisson-Hamiltonian reduction of the classical limit.

The existence of quantum momentum maps is only known in very few cases, like linear Poisson structures and symplectic manifolds. The aim of this talk is to fill this gap and show that there is a universal way to find quantized momentum maps using so-called adapted formality morphisms which exist, if one considers nice enough Lie group actions. This is a joint work with Chiara Esposito, Ryszard Nest and Boris Tsygan.

Montag,
2024-06-03
16:15-17:45 Uhr
Raum 125, Ernst-Zermelo-Str. 1
Nadine Große: On local boundary conditions for Dirac-type operators

We give an overview on smooth local boundary conditions for Dirac-type operators, giving existence and non-existence results for local symmetric boundary conditions. We also discuss conditions when the boundary conditions are elliptic/regular/Shapiro-Lopatinski (i.e. in particular giving rise to self-adjoint Dirac operators with domain in $H^1$). This is joint work with Hanne van den Bosch (Universidad de Chile) and Alejandro Uribe (University of Michigan).

Montag,
2024-06-10
16:15-01:15 Uhr
Raum 125, Ernst-Zermelo-Str. 1
Christian Ketterer: Ricci curvature, metric measure spaces and the Riemannian curvature-dimension condition

I explain idea of synthetic Ricci curvature bounds for metric measure spaces and one of their applications in Riemannian geometry.

Montag,
2024-06-17
16:15 Uhr
Raum 125, Ernst-Zermelo-Str. 1
Jonah Reuß: A necessary condition for zero modes of the Dirac equation

We will state a necessary condition for the existence of a non-trivial solution of the Dirac equation, which is based on a Euclidean-Sobolev-type inequality. First, we will state the theorem in the flat setting and give an overview of the technical issues of the proof. Afterwards, we will consider and point out the main differences in the not necessarily flat setting. This talk is based on a work by R.Frank and M.Loss.


Abonnieren

Die Einträge dieser Veranstaltung können im iCalender Format abonniert werden. die URL dazu lautet:
http://wochenprogramm.mathematik.uni-freiburg.de/ical/SS2024/OS-DiffGeo.ics