Vorträge in der Woche 06.02.2023 bis 12.02.2023
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Dienstag, 07.02.2023: Mathematische Beweise lesen lernen: Wie Toulmins Argumentationstheorie und linguistische Textebenen unseren Blick auf Leseprozesse schärfen können
Verena Spratte (Universität Göttingen)
Mathematische Beweise sind zugleich Idealbild und pathologischer Grenzfall in Toulmins allgemeiner Argumentationstheorie, da sie nur notwendige und keine ungewissen Schlussfolgerungen zulassen. Wie kann die Behandlung solcher Fachtexte im Rahmen des Mathematikunterrichts zur Allgemeinbildung beitragen? Um Chancen und Grenzen zu präzisieren, verwenden wir verschiedene Textebenen aus der linguistischen Forschung zum Leseverständnis. Betrachtet man diese Textebenen zusammen mit den Charakteristika der mathematischen Textgattung „Beweis“, so entsteht ein Modell für Beweisverständnis, das wir in den bisherigen Forschungskontext einordnen werden. Erste empirische Ergebnisse zeigen sein Potential für Unterrichtsplanung und -forschung.
| Uhrzeit: | 14:15 |
| Ort: | MINT Klassenraum (F-Bau, Ebene 4) |
| Gruppe: | MINT-Forum |
| Einladender: | J.-P. Burde, W. Paravicini, S. Schwarzer |
Dienstag, 07.02.2023: Condensed abelian groups
Matilde Manzaroli
Es gibt Tee ab 13:45 im Büro CA526.
| Uhrzeit: | 14:15 |
| Ort: | C9A03 |
| Gruppe: | Seminar zur Kondensierten Mathematik |
| Einladender: | A.Deitmar, H.Markwig |
Mittwoch, 08.02.2023: Hodge numbers of moduli stacks of principal bundles
Florent Schaffhauser, U. Heidelberg
The Poincaré series of moduli stacks of semistable G-bundles on curves has been computed by Laumon and Rapoport. In this joint work with Melissa Liu, we show that the Hodge-Poincaré series of these moduli stacks can be computed in a similar way. As an application, we obtain a new proof of a joint result of the speaker with Erwan Brugallé, on the maximality on moduli spaces of vector bundles over real algebraic curves.
| Uhrzeit: | 10:30 - 11:30 |
| Ort: | C4H33 |
| Gruppe: | Oberseminar kombinatorische algebraische Geometrie |
| Einladender: | Daniele Agostini, Hannah Markwig |
Donnerstag, 09.02.2023: On the approximation of null hypersurfaces via maximal surfaces
Albachiara Cogo (Tübingen)
Maximal surfaces are spacelike hypersurfaces of a Lorentzian manifold which are critical points of the area functional. They are very important tools in General Relativity and can be studied by apply-ing non-linear PDEs techniques since the Euler-Lagrange equation of the variational problem of maximization of the area is a quasi-linear elliptic PDE that geometrically describes the vanishing of the mean curvature. Given the behavior of some simple solutions in Minkowski spacetime, it seems natural to investigate when sequences of maximal surfaces on exterior domains converge to null hypersurfaces. We will present some developments in this direction, referring to my ongoing Ph.D. project.
| Uhrzeit: | 14:00 |
| Ort: | S 9 (C 06 H 05) and virtual via zoom, for zoom link please contact Martina Jung or Martina Neu |
| Gruppe: | Oberseminar Geometrische Analysis, Differentialgeometrie und Relativitätstheorie |
| Einladender: | Prof. Dr. Carla Cederbaum, Dr. Melanie Graf, Prof. Dr. Gerhard Huisken (Tübingen), together with Prof. Dr. Jan Metzger (Potsdam) |
Donnerstag, 09.02.2023: Pseudo-monotone operator theory for electro-rheological fluids
Alex Kaltenbach (Universität Freiburg)
We consider a model describing the unsteady motion of an incompressible, electro-rheological fluid. Due to the time-space-dependence of the power-law index, the analytical treatment of this system is involved. Standard results like a Poincare or a Korn inequality are not available. Introducing natural energy spaces and constructing suitable smoothing methods, we establish the validity of a formula of integration-by-parts which allows to extend the classical theory of pseudo-monotone operators to the framework of variable Bochner-Lebesgue spaces. This leads to generalised notions of pseudo-monotonicity and coercivity, the so-called Bochner pseudo-monotonicity and Bochner coercivity. With the aid of these notions and the established formula of integration-by-parts it is possible to prove an abstract existence result which immediately implies the weak solvability of the model describing the unsteady motion of an incompressible, electro-rheological fluid.
| Uhrzeit: | 14:15 |
| Ort: | 1B01, Hörsaalzentrum |
| Gruppe: | Oberseminar Numerik |
| Einladender: | Prohl, Lubich |
Donnerstag, 09.02.2023: Causal Perturbation Theory
Matthias Isele (Tübingen)
The predictions of Quantum Field Theory are part of the greatest triumphs in physics. The fundamental physical nature, e.g. the description of elementary particles, may attract the interested mathematician. However, in standard literature, they find themselves exposed to rather dubious mathematics; Distributions are evaluated pointwise, time-ordered products are ill-defined, scattering amplitutes diverge at almost any order. Finite predictions are extracted by "regularizing" and "renormalizing" divergent loop integrals. Luckily, a rigorous (and fairly unknown) alternative approach to Quantum Field Theory has already been discovered: Causal Pertubation Theory! In short, Causal Pertubation Theory determines the scattering matrix of a Quantum Field Theory inductively from a first order input. The main ingredient is the so-called causality condition (instead of a Schrödinger equation), which fixes the scattering matrix essentially uniquely. Nowhere do ill-defined quantities appear and the predictions are identical to the standard approach. In this talk I will outline the basic ideas and tools of Causal Pertubation Theory. Afterwards you can (in principle) perform every computation found in standard literature to Quantum Field Theory, but on a rigorous level!
| Uhrzeit: | 14:30 |
| Ort: | C4H33 |
| Gruppe: | Oberseminar Mathematical Physics |
| Einladender: | Capel, Keppeler, Lemm, Pickl, Teufel, Tumulka |