The group configuration in stable theories
Dienstag, 3.5.22, 14:30-15:30, Raum 404, Ernst-Zermelo-Str. 1
A group configuration is a geometric incidence configuration consisting of 6 points which in stable theories is related to the existence of a type definable group. In the first part of the talk, we will introduce the above concepts and point out why a group gives rise to a group configuration. Moreover, by a result from Hrushovski, any group configuration in a stable theory yields the existence of a type definable group. We will discuss the basic ideas of this proof. The second part of the talk will present an application. Hrushovski and Pillay showed that any definable group in a real closed field F is locally isomorphic to the F-rational points of an algebraic group defined over F. This is achieved by considering a group configuration of the group in the algebraic closures of F.
Lower bounds for the transversal Ricci curvature of a Riemannian foliation via entropy convexity
Dienstag, 3.5.22, 16:00-17:00, Raum 127, Ernst-Zermelo-Str. 1
The transversal Ricci curvature of a Riemannian foliation\nis the trace of the transversal Riemannian curvature tensor on the associated normal bundle of the leaves. Lower bounds for the transversal Ricci tensor, for instance, imply estimates for the first eigenvalue of the basic Laplacian by results of Richardson. In this talk we will see that transversal lower Ricci bounds imply (and in some cases also require) entropy convexity estimates along special Kantorovich Rubinstein geodesics. A correction term that involves the mean curvature vector of the leaves will play a special role.
Donnerstag, 5.5.22, 15:15-16:15, Hörsaal II, Albertstr. 23b
Reshetikhin-Turaev representations as Kähler local systems
Freitag, 6.5.22, 10:30-11:30, Hörsaal II, Albertstr. 23b
From a joint work, partially in progress, with Louis Funar. In Orbifold Kähler Groups related to Mapping Class groups, arXiv:2112.06726, we constructed certain orbifold compactifications of the moduli stack of stable pointed curves labelled by an integer p such that the corresponding Reshetikhin Turaev representation of the mapping class group descends to a representation of the orbifold fundamental group. I will explain the construction of that orbifold and why it is uniformizable. I will then report on a work in progress on the uniformization of these orbifolds. I will sketch a proof of the steiness of its universal covering p odd large enough. An interesting new quantum topological consequence is that the image of the fundamental group of the smooth base of a non isotrivial complex algebraic family of smooth complete curves of genus greater than 2 by the Reshetikhin-Turaev representation is infinite (generalizing the Funar-Masbaum and the Koberda-Santharoubane-Funar-Lochak infiniteness theorems).
General relativity, spectral theory, and microlocal analysis
Donnerstag, 12.5.22, 17:00-18:00, Hörsaal II, Albertstr. 23b
A central problem in General Relativity is to describe the behavior of various spacetimes, such as flat spacetimes or black holes, under perturbations. I will describe recent results related to the stability of black holes, with particular emphasis on the roles played by spectral theory and microlocal analysis.\n\n
... und wie erklärst du?
Dienstag, 17.5.22, 19:30-20:30, Hörsaal II, Albertstr. 23b
\nFragt man Schülerinnen und Schüler, was eine gute Lehrkraft auszeichnet, nennen diese zumeist die Fähigkeit, gut erklären zu können. Doch was zeichnet verständliche und lernförderliche Erklärungen aus? Worauf sollten Lehrkräfte achten, wenn Sie Erklärungen für Schülerinnen und Schüler formulieren? Woran liegt es, dass viele Lehrkräfte durchaus in der Lage sind, gut zu erklären, dies jedoch im Schulkontext oftmals trotzdem nicht tun? Diesen und weiteren Fragen geht Frau Dr. Weinhuber in ihrem interaktiven Vortrag nach.
Lifting globally F-split surfaces over the Witt vectors
Freitag, 20.5.22, 10:30-11:30, Hörsaal II, Albertstr. 23b
Given a projective variety X over an algebraically closed field k of characteristic p, it is natural to understand the possible geometric and arithmetic obstructions to the existence of a lifting to characteristic zero. Motivated by the case of abelian manifolds and K3 surfaces, a folklore conjecture claims that ordinary Calabi-Yau manifolds should admit a lifting over the ring of Witt vectors W(k). I will report a joint work with I. Brivio, T. Kawakami and J. Witaszek where we show that globally F-split surfaces (which can be thought of as log Calabi-Yau surfaces that behave arithmetically well) are liftable over W(k) and we deduce several geometric consequences (as the Bogomolov bound on the number of singular points of klt del Pezzo F-split surfaces).
Workshop on Nonlinear Bending
Montag, 23.5.22, 09:00-10:00, Raum 226, Hermann-Herder-Str. 10
Shape transitions in non-Euclidean ribbons
Montag, 23.5.22, 09:30-10:30, Raum 226, Hermann-Herder-Str. 10
Mechanical properties of plants: structural background and what can be learnt for biomimetic applications
Montag, 23.5.22, 14:00-15:00, Raum 226, Hermann-Herder-Str. 10
Numerical Approximations of Thin Structures Undergoing Large Deformations
Montag, 23.5.22, 15:50-16:50, Raum 226, Hermann-Herder-Str. 10
Homogeneous G-structures
Montag, 23.5.22, 16:15-17:15, Online / SR 125
G-structures unify several interesting geometries including: almost complex, Riemannian, almost symplectic geometry, etc., the integrable versions of which being complex, flat Riemannian, symplectic geometry, etc. Contact manifolds are odd dimensional analogues of symplectic manifolds but, despite this, there is no natural way to understand them as manifolds with an ordinary integrable G-structure. In this talk, we present a possible solution to this discrepancy. Our proposal is based on a new notion of homogeneous G-structures. Interestingly, besides contact, the latter include other nice (old and new) geometries including: cosymplectic, almost contact, and a curious “homogeneous version” of Riemannian geometry. This is joint work with A. G. Tortorella and O. Yudilevich.
Wrinkles in nature and technology
Dienstag, 24.5.22, 09:30-10:30, Raum 226, Hermann-Herder-Str. 10
Understanding the mechanical interaction of plants with their environment
Dienstag, 24.5.22, 14:00-15:00, Raum 226, Hermann-Herder-Str. 10
Classes of graphs characterizable by finitely many homomorhism counts
Dienstag, 24.5.22, 14:30-15:30, Raum 404, Ernst-Zermelo-Str. 1
In 1967 Lovász showed that up to isomorphism every finite relational structure A is determined by the homomorphism counts hom(B,A), i.e, by the number of homomorphisms from B to A, where B ranges over all structures (of the same vocabulary as A).\nMoreover, it suffices that B ranges over the structures with at most as many elements as A.\n\nIn the talk, we deal with classes C of graphs characterizable by finitely many homomorphism counts, i.e., classes for which there are finitely many graphs F1,...,Fk such that for every graph G already hom(F1,G),...,hom(Fk,G) determines whether G is in C. Among others, we show which prefix classes of first-order logic have the property that each class of graphs definable by a sentence of this prefix class is characterizable by finitely many homomorphism counts.\n\n
Design of origami structures with curved tiles between the creases
Dienstag, 24.5.22, 15:50-16:50, Raum 226, Hermann-Herder-Str. 10
Agent-Based Modelling of Single Cell Variability of CRISPR-Cas Interference and Adaptation
Freitag, 27.5.22, 12:00-13:00, online: Zoom
The strong Homotopy Structure of Phase Space Reduction in Deformation Quantization
Montag, 30.5.22, 16:15-17:15, Raum 125, Ernst-Zermelo-Str. 1
A Hamiltonian action on a Poisson manifold induces a Poisson structure on a reduced manifold,\ngiven by the Poisson version of the Marsden-Weinstein reduction or equivalently the BRST-method.\nFor the latter there is a version in deformation quantization for equivariant star products, i.e. invariant\nunder the action and admitting a quantum momentum map which produces a star product on the\nreduced manifold.\nFixing a Lie group action on a manifold, one can define a curved Lie algebra whose Maurer-Cartan\nelements are invariant star products together with quantum momentum maps. Star products on the\nreduced manifold are Maurer-Cartan elements of the usual DGLA of polydifferential operators. Thus,\nreduction is just a map between these two sets of Maurer-Cartan elements. In my talk I want to show\nthat one can construct an \(L_\binfty\)-morphism, which on the level of Maurer Cartan elements provides a\nreduction map.\nThis a joint work with Chiara Esposito and Andreas Kraft (arXiv: 2202.08750).
The space of types with a spectral topology
Dienstag, 31.5.22, 14:30-15:30, Raum 404, Ernst-Zermelo-Str. 1
Influenced by results in real algebraic geometry, Pillay pointed out in 1988 that the space of types of an o-minimal expansion of a real closed field admits a spectral topology. With this topology, this space is quasi-compact and T_0, yet not Hausdorff. Nonetheless, the subspace of all closed points turns out to be quasi-compact and Hausdorff. \n\nIn this talk, I will relate the space of closed points with other topological spaces, such as the space of mu-types considered first by Peterzil and Starchenko. In addition, I will explain how to characterize coheir types of an o-minimal expansion of a real closed field within invariant types, using the spectral topology.\n\n
Beweise als Imitationsgrundlage
Dienstag, 31.5.22, 19:30-20:30, Online-Vortrag
\nBeim Betreiben von Mathematik, insbesondere beim Definieren, Analogisieren und Generalisieren, greifen wir typischerweise auf vorhandene Beweise zurück. Wir versuchen diese auf unbekanntes Terrain zu übertragen und dabei so weit wie möglich an den Beweisideen festzuhalten. Die bestehenden Beweise bieten unserem Denken bei der Suche nach geeigneten Definitionen und interessanten Sätzen eine Orientierung. Dass Beweise im Kontext des Entdeckens nicht nur Ziel, sondern auch Ausgangspunkt und Werkzeug mathematischer Betrachtungen sein können, ist eine bezogen auf das Wesen der Mathematik grundlegende Einsicht, deren schulische Vermittlung fortwährend didaktische Aufmerksamkeit verdient. Im Vortrag soll die hier angesprochene entdeckende Funktion von Beweisen an einfachen elementarmathematischen Beispielen entfaltet werden.