Vorträge in der Woche 05.12.2022 bis 11.12.2022

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Dienstag, 06.12.2022: Mean equicontinuity beyond minimality

Till Hauser (MPI Bonn)

In this talk we present recent developments and new results in the study of mean equicontinuity and weak mean equicontinuity in the context of countable discrete amenable groups, such as a characterization in terms of spectral theory. It is known that the notions of mean eq. and weak mean eq. do not depend on the process of averaging (the Følner sequence), whenever the action is minimal, or the acting group is Abelian. However, we present an example of a (non-minimal, but transitive) action where mean equicontinuity and weak mean equicontinuity do depend on the process of averaging. This observation leads to the new notions of essential mean equicontinuity and essential weak mean equicontinuity, for which we present characterizations.

Uhrzeit: 12:30
Ort: Online (Zoom) siehe https://ergodic.de
Gruppe: Operator Theoretic Aspects of Ergodic Theory (OTET)
Einladender: R. Nagel

Mittwoch, 07.12.2022: Klassifikation und Untersuchung algebraischer Varietäten nach ihren kombinatorischen Daten

Victor Batyrev

In dem Vortrag präsentiere ich die Ergebnisse und die offenen Fragen in den kombinatorischen Untersuchungen torischer Hyperflächen, die durch das Mori-Programm und die Spiegelungssymmetrie inspiriert sind.

Uhrzeit: 10:30 - 11:30
Ort: C4H33
Gruppe: Oberseminar kombinatorische algebraische Geometrie
Einladender: Daniele Agostini, Hannah Markwig

Donnerstag, 08.12.2022: Global hyperbolicity through the eyes of the null distance

Leonardo Garcia Heveling

Can one encode the causal information of a spacetime in a metric space structure? In 2016, Sormani and Vega conjectured how this may be done. In this talk, I will present some recent results confirming that the answer is yes. Not only can the causal relation be encoded, but also the condition of global hyperbolicity can be characterized via completeness of the corresponding metric space. This is joint work with Annegret Burtscher.

Uhrzeit: 14:15
Ort: S 9 (C06H05) und über Zoom. Den Zoom-Link erhalten Sie per E-Mail von Frau Martina Jung oder Frau Martina Neu. For participating online, please sign up by sending an email to Martina Jung or Martina Neu.
Gruppe: Oberseminar Geometrische Analysis, Differentialgeometrie und Relativitätstheorie
Einladender: Carla Cederbaum, Melanie Graf, Gerhard Huisken, zusammen mit Jan Metzger (Potsdam)

Donnerstag, 08.12.2022: Classical spin Hamiltonians are context-sensitive languages

Sebastian Stengele (Universität Innsbruck)

Classical spin Hamiltonians are a powerful tool to model complex systems, characterized by a local structure given by the local Hamiltonians. One of the best understood local structures is the grammar of formal languages, which are central in computer science and linguistics, and have a natural complexity measure given by the Chomsky hierarchy. If we see classical spin Hamiltonians as languages, what type of grammar do the local Hamiltonians correspond to? Here we show how to cast classical spin Hamiltonians as formal languages, and classify them in the Chomsky hierarchy. We prove that the language of (effectively) zero-dimensional spin Hamiltonians is regular, one-dimensional spin Hamiltonians is deterministic context-free, and higher-dimensional and all-to-all spin Hamiltonians is context-sensitive. This provides a new complexity measure for classical spin Hamiltonians, which captures the hardness of recognizing spin configurations and their energies.

Uhrzeit: 14:30
Ort: C4H33
Gruppe: Oberseminar Mathematical Physics
Einladender: Capel, Keppeler, Lemm, Pickl, Teufel, Tumulka

Donnerstag, 08.12.2022: Edgeworth expansion for the weakly interacting Bose gas

Dr. Lea Boßmann (LMU)

We consider the ground state and the low-energy excited states of a system of weakly interacting bosons. We derive an Edgeworth expansion for the fluctuations of bounded one-body operators around the condensate, which yields corrections to a central limit theorem. This is a joint work with Sören Petrat.

Uhrzeit: 16:00
Ort: C3N14
Gruppe: Oberseminar Mathematical Physics
Einladender: Capel, Keppeler, Lemm, Pickl, Teufel, Tumulka

Freitag, 09.12.2022: Higgs bundles, affine spheres, Monge-Ampere equations, and SYZ mirror symmetry

Prof. Franz Pedit (University of Massachusetts Amherst)

In this talk I shall explain how to construct special Lagrangian 3-torus fibrations, singular over a trivalent discriminant locus, of Calabi-Yau 3-folds using parabolic non-Abelian Hodge theory. Along the way, we shall encounter Monge-Ampere equations and very classical differential geometric objects, the affine spheres introduced by the Blaschke school in the 1930s. The Strominger-Yau-Zaslow approach to mirror symmetry suggests existence of such fibrations in Calabi-Yau manifolds based on string/brane dualities. The results are joint work with Sebastian Heller (Yau Institute Beijing) and Charles Ouyang (UMass Amherst).

Uhrzeit: 17:15 - 18:15
Ort: N 14
Gruppe: Kolloquium
Einladender: Bohle, Loose