Vorträge in der Woche 31.10.2022 bis 06.11.2022
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Mittwoch, 02.11.2022: Real Double Hurwitz Numbers with pairs of complex conjugate branch points
Paul Vögele ( Tübingen)
We study the count of real ramified covers of P^1 with given ramification data. In particular, we discuss a nice correspondence between classical and tropical real double Hurwitz Numbers, mediated by monodromy representations in the symmetric group and monodromy graphs.
| Uhrzeit: | 10:30 - 11:30 |
| Ort: | C4H33 |
| Gruppe: | Oberseminar Kombinatorische Algebraische Geometrie |
| Einladender: | Daniele Agostini / Hannah Markwig |
Donnerstag, 03.11.2022: 2D limit models in nonlinear elasticity: membranes, plates and Willmore surfaces
Claudia Grabs (Universität Potsdam)
Elastic deformations of thin plates include stretching, shearing and compression, as well as bending. As the thickness of the plate goes to zero, different limit theories arise, depending on the scaling of the elastic energy with the thickness of the plate for different deformations. Following an introduction to the basics of 3D nonlinear elasticity, including convexity conditions and existence theorems, we turn to 2D nonlinear elasticity. First we introduce the membrane model, capturing the stretching of an elastic membrane. We show how this is obtained either as Gamma-limit from 3D elasticity or derived from purely 2D conservation laws. For bending deformations of an elastic plate the nonlinear bending theory is obtained by Gamma convergence. As a special case here, the Willmore functional arises.
| Uhrzeit: | 14:00 |
| Ort: | S 9 (C 06 H 05) und über Zoom. Den Zoom-Link erhalten Sie per E-Mail von Frau Martina Jung oder Frau Martina Neu. |
| Gruppe: | Oberseminar Geometrische Analysis, Differentialgeometrie und Relativitätstheorie |
| Einladender: | Carla Cederbaum, Melanie Graf, Gerhard Huisken, Jan Metzger (Potsdam) |
Donnerstag, 03.11.2022: Lefschetz and Unimodality for IDP Lattice Polytopes
Johanna Steinmeyer (Hebrew University of Jerusalem und University of Copenhagen)
One of the fundamental questions of Ehrhart theory lies in characterizing the possible $h^*$-polynomials of Lattice Polytopes. One discovers especially nice structures if the polytope is reflexive and if its associated semigroup is generated in degree 1. In this case, Hibi and Ohsugi conjectured that the coefficients of the $h^*$-polynomial — which is to say, the $2k$-th stringy Betti numbers of the Fano variety — are always unimodal. We present a proof of this conjecture by establishing generic anisotropy and strong Lefschetz properties in the associated semigroup algebras. As a bonus, we also get unimodality for the $\tilde{S}$-polynomials — the building blocks of the stringy E-function. Based on joint work with Adiprasito, Papadakis, and Petrotou; arxiv:2210.10734.
| Uhrzeit: | 14:00 |
| Ort: | N15 (M2) |
| Gruppe: | Oberseminar Algebraische Geometrie |
| Einladender: | V. Batyrev, J. Hausen, Th. Markwig |
Donnerstag, 03.11.2022: Relativistic elasticity and compactness bounds
José Natário (Instituto Superior Técnico, Universidade de Lisboa)
After reviewing the basics of relativistic elasticity theory, I will introduce a general framework to study spherically symmetric self-gravitating elastic bodies systematically within general relativity, and apply it to investigate compactness bounds in this context.
| Uhrzeit: | 15:30 |
| Ort: | online - wenn Sie Zugang haben wollen, schicken Sie bitte eine Nachricht an Martina Jung |
| Gruppe: | Oberseminar |
| Einladender: | Prof. Dr. Carla Cederbaum |
Donnerstag, 03.11.2022: Diophantische Gleichungen und die Riemannsche Vermutung
Prof. Dr. Baruch Moroz
Eine neue Arbeit von Yu.V. Matiyasevich erlaubt es uns, einige relativ einfache Diophantische Gleichungen zu konstruieren, die eng mit der Riemannschen Vermutung verbunden sind. Ich werde über solche und ähnliche Gleichungen sprechen.
| Uhrzeit: | 16:00 |
| Ort: | C4H33 |
| Gruppe: | Oberseminar Algebraische Geometrie |
| Einladender: | Batyrev, Hausen, Th. Markwig |