Thursday, 1.11.12, 17:00-18:00, Hörsaal II, Albertstr. 23b
Bogomolov-Sommese Vanishing on log canonical pairs
Friday, 2.11.12, 10:00-11:00, Raum 404, Eckerstr. 1
Fibrewise Morse functions and higher torsion invariants
Monday, 5.11.12, 16:15-17:15, Raum 404, Eckerstr. 1
I will give a short overview about higher torsion invariants\nfor families of compact manifolds. Then I will sketch a generalisation of Igusa-Klein torsion that has similar properties as Bismut-Lott torsion. This is the first step in the comparison of the two invariants.
Density and regularity results for flat isometric immersions
Wednesday, 7.11.12, 16:15-17:15, Hörsaal II, Albertstr. 23b
This talk is about isometric immersions from a two-dimensional domain (endowed with the standard flat metric in R^2) into R^3. I will present in some detail the proof of the following density result: every isometric immersion with square integrable second fundamental form can be approximated by isometric immersions which are smooth up to the boundary of the domain. This result is a key ingredient, e.g., in the derivation of several thin-film models from three dimensional elasticity. \nIf time allows, I will also briefly present an optimal regularity result about isometric immersions minimizing the Willmore functional.\n
Indiscernibles
Wednesday, 7.11.12, 16:30-17:30, Raum 404, Eckerstr. 1
We give a simple proof of Shelah's theorem on the existence\nof tree indiscernibles.
Thursday, 8.11.12, 17:00-18:00, Hörsaal II, Albertstr. 23b
Gromov Witten Invariants for the Hilbert scheme of points of a K3 surface
Friday, 9.11.12, 10:00-11:00, Raum 404, Eckerstr. 1
The Yau-Zaslow formula gives an expression of the number of nodal rational curves on a K3 surface in terms of a modular form. In this talk we explain how to extend their result to the Hilbert scheme of 2 points of a K3 surface. In particular, we will present the generating series for the reduced genus 0 GW Invariants which will be given by a weak Jacobi Form.\n
Floer theory and Gromov-Witten theory
Monday, 12.11.12, 16:00-17:00, Raum 404, Eckerstr. 1
In his proof of the Arnold conjecture about the number of fixed points of Hamiltonian symplectomorphisms, A. Floer developed a new infinite-dimensional version of Morse homology. While the chain groups are generated by these fixed points, the differential counts pseudoholomorphic sections, which in turn provides a link to Gromov-Witten theory. In my talk I will introduce the basic concepts of Floer homology and its application to the Arnold conjecture. At the end I plan to sketch the main results of my recent paper 1206.1564, where I was able to complete the correspondence between rational Gromov-Witten theory and Floer theory of symplectomorphisms.
A nonlinear PDE system for phase separation and damage
Tuesday, 13.11.12, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Über stochastische Exponentiale stetiger lokaler Martingale
Thursday, 15.11.12, 17:00-18:00, Hörsaal II, Albertstr. 23b
Eine Zusammenfassung findet sich auf:\n\nhttp://logik.mathematik.uni-freiburg.de/vorlesungen/ws12/kolloquium1511_2012.pdf
Drinfeld modules and their application to factoring polynomials
Friday, 16.11.12, 10:00-11:00, Raum 404, Eckerstr. 1
Major works done in Function Field Arithmetic show a strong analogy between the ring of integers Z and the ring of polynomials over a finite field Fq[T]. While an algorithm has been discovered to factor integers using elliptic curves, the discovery of Drinfeld modules, which are analogous to elliptic curves, made it possible to exhibit an algorithm for factorising polynomials in the ring Fq[T]. \nIn this talk, we introduce the notion of Drinfeld modules, then we demonstrate the analogy between Drinfeld modules and Elliptic curves. Finally, we present an algorithm for factoring polynomials over a finite field using Drinfeld modules.\n
Vafa-Witten Estimates
Monday, 19.11.12, 16:00-17:00, Raum 404, Eckerstr. 1
In 1984 Vafa and Witten developed a method to find an upper bound for the first eigenvalue of a Dirac-Operator. After giving short introduction to the topic, I will explain the connection between Vafa-Witten Estimates and L-infinity variational problems. We will also see a geometric version of a sharp estimate on the projective space.
Monday, 19.11.12, 16:15-17:15, Raum 404, Eckerstr. 1
Thursday, 22.11.12, 17:00-18:00, Hörsaal II, Albertstr. 23b
Motives of Deligne-Mumford Stacks
Friday, 23.11.12, 10:00-11:00, Raum 404, Eckerstr. 1
For every smooth and separated Deligne-Mumford stack F,\nwe will associate a motive M(F) in Voevodsky's category of mixed motives with rational coecients DM^eff(k; Q). For F proper over a field of characteristic 0, we will compare M(F) with the Chow motive associated to F by Toen. Without the properness condition we will show that M(F) is a direct summand of the motive of a smooth quasi-projective\nvariety. Then we will generalize a motivic decomposition theorem due to Karpenko to relative geometrically cellular Deligne-Mumford stacks.\nThis will depend on a vanishing result of Voevodsky. Even in the classical case, our method yields a simpler and more conceptual proof of Karpenko's result.
On the structure of closed currents of finite mass
Monday, 26.11.12, 16:15-17:15, Raum 404, Eckerstr. 1
Introduction to Vafa-Witten Estimates
Monday, 26.11.12, 16:15-17:15, Raum 404, Eckerstr. 1
1984 Vafa and Witten developed a method to obtain upper bounds for the first eigenvalue of a Dirac-Operator on a compact manifold. I will explain the method and the related geometry in detail. We will see an example of an optimal Vafa-Witten bound on the projective space obtained by geometric arguments.\nFurthermore, I will give a connection between the Vafa-Witten method and L-infinity variational problems.
Silver measurabilty without Miller measurability
Wednesday, 28.11.12, 16:30-17:30, Raum 404, Eckerstr. 1
In the 1980s, Shelah invented a deep and rather mysterious \nconstruction to build strongly homogeneous algebra, called amalgamation. \nTogether with the notion of sweet forcing, it was the amazing technique to\nget \na model where all sets have the Baire property, without using inaccessible \ncardinals. The aim of the talk is to present an (absolutely less ambitious) \napplication of Shelah´s amalgamation to obtain a model where all sets are \nSilver measurable but there exists a non-Miller measurable set. \n
Thursday, 29.11.12, 17:00-18:00, Hörsaal II, Albertstr. 23b
Rational volume of varieties over complete local fields and Galois extensions
Friday, 30.11.12, 10:00-11:00, Raum 404, Eckerstr. 1
We are interested in the following question: When does a given variety over a complete local field K have a rational point? The rational volume is a motivic invariant of a K-variety X vanishing if X has no K-rational point. For a tame Galois extension L over K, we will compare the rational volume of a K-variety X and of its base change XL to L. To do so, we construct out of a given weak Néron model of XL with an action of the Galois group of L over K a weak Néron model of X with some universal property. As an application, we will show that some varieties over K with potential good reduction have K-rational points.