Eröffnung
Montag, 22.10.12, 15:00-16:00, Hörsaal 1, Physik-Hochhaus, Hermann-Herder-Str. 3a
Curve/sheaf correspondence for Calabi-Yau 3-folds
Montag, 22.10.12, 15:30-16:30, Hörsaal 1, Physik-Hochhaus, Hermann-Herder-Str. 3a
Montag, 22.10.12, 16:15-17:15, Raum 404, Eckerstr. 1
Automorphisms of Drinfeld's half-spaces over a finite field
Montag, 22.10.12, 17:15-18:15, Hörsaal 1, Physik-Hochhaus, Hermann-Herder-Str. 3a
Spuren singulärer Moduli
Mittwoch, 24.10.12, 16:00-17:00, Hörsaal Rundbau, Albertstr. 21a
Donnerstag, 25.10.12, 17:00-18:00, Hörsaal II, Albertstr. 23b
Donnerstag, 25.10.12, 17:00-18:00, Hörsaal II, Albertstr. 23b
NN
Montag, 29.10.12, 16:15-17:15, Raum 404, Eckerstr. 1
Variational characteristics of pesudo-holomorphic curves in symplectic manifold
Dienstag, 30.10.12, 16:15-17:15, Raum 404, Eckerstr. 1
\nThis talk consists of two parts. First, I will give an overview on symplectic mean curvature flows. Then I will talk about a variational characteristic of pseudo-holomorphic curves in symplectic manifold. The latter one is a recent result jointed with C. Arezzo.\n
Combinatorics with block sequences
Mittwoch, 31.10.12, 16:30-17:30, Raum 404, Eckerstr. 1
Combinatorics with block sequences
Mittwoch, 31.10.12, 16:30-17:30, Raum 404, Eckerstr. 1
Donnerstag, 1.11.12, 17:00-18:00, Hörsaal II, Albertstr. 23b
Bogomolov-Sommese Vanishing on log canonical pairs
Freitag, 2.11.12, 10:00-11:00, Raum 404, Eckerstr. 1
Fibrewise Morse functions and higher torsion invariants
Montag, 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
Mittwoch, 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
Mittwoch, 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.
Donnerstag, 8.11.12, 17:00-18:00, Hörsaal II, Albertstr. 23b
Gromov Witten Invariants for the Hilbert scheme of points of a K3 surface
Freitag, 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
Montag, 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
Dienstag, 13.11.12, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Über stochastische Exponentiale stetiger lokaler Martingale
Donnerstag, 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
Freitag, 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
Montag, 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.
Montag, 19.11.12, 16:15-17:15, Raum 404, Eckerstr. 1
Donnerstag, 22.11.12, 17:00-18:00, Hörsaal II, Albertstr. 23b
Motives of Deligne-Mumford Stacks
Freitag, 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
Montag, 26.11.12, 16:15-17:15, Raum 404, Eckerstr. 1
Introduction to Vafa-Witten Estimates
Montag, 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
Mittwoch, 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
Donnerstag, 29.11.12, 17:00-18:00, Hörsaal II, Albertstr. 23b
Rational volume of varieties over complete local fields and Galois extensions
Freitag, 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.
Free fermions and tau-functions
Montag, 3.12.12, 16:15-17:15, Raum 404, Eckerstr. 1
The formalism of free fermions \nused for construction of tau-functions of classical \nintegrable hierarchies is reviewed.\nWe give a derivation of \ngroup-like properties of the normally ordered exponents, \ntransformations between different normal orderings,\nthe bilinear identity and the generalized Wick's\ntheorem. We also consider various examples of tau-functions\nand give their fermionic realization.
Modeling and simulation of fluid-structure interaction in haemodynamics
Dienstag, 4.12.12, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
We consider the fluid-structure interaction problem arising in\nhaemodynamic applications where the blood interacts with the arterial\nwall. Blood dynamics is described by the Navier-Stokes equations for\nNewtonian fluids, conveniently rewritten in Arbitrary Lagrangian\nEulerian (ALE) formulation to account for the deformation of the fluid\ndomain boundary; arterial dynamics is described by non-linear\nfinite elasticity equations.\n\nWe consider partitioned algorithms based on Robin interface conditions\nto solve numerically the fluid-structure interaction problem. At each\ntime step the non-linear or linearized fluid and structure subproblems\nare solved iteratively until convergence and linear combinations of\nvelocities and normal stresses (Robin interface conditions) are\nexchanged at the common interface. In particular, we discuss suitable\nchoices of the coefficients in the Robin conditions based on reduced\nmodels and show how the optimized Robin conditions greatly reduce the\neffect of added mass on the convergence of the iterative algorithm.\n\nWe present finally some simulations of blood flow in carotid\nbifurcations reconstructed from MRI data, from patients having\natherosclerotic plaques, before and after the plaque removal.\n\nReferences\n\n[1] S. Badia, F. Nobile, and C. Vergara (2008). Fluid-structure\npartitioned procedures based on Robin transmission\nconditions. J. Comp. Phy 227, 7027–7051.\n\n[3] P. Causin, J. Gerbeau, and F. Nobile (2005). Added-mass effect in\nthe design of partitioned algorithms for fluid-structure\nproblems. Comput. Methods Appl. Mech. Engrg 194(42-44), 4506– 4527.\n\n[4] F. Nobile, M. Pozzoli, C. Vergara, Exact and inexact partitioned\nalgorithms for fluid-structure interaction problems with finite\nelasticity in haemodynamics, MOX Report 37/2012, submitted.
Symplectic tools for studying quantum entanglement
Dienstag, 4.12.12, 15:45-16:45, Hörsaal 1, Physik Hochhaus, Hermann-Herder-Straße 3
A description for non-specialists of the mathematical tools which have been recently implemented in the development of measuring devices for degrees of quantum entanglement will be given. These methods involve symmetry considerations in representation theoretic settings. The talk will conclude\nwith a survey of recent results.\n
Confined structures of least bending energy
Mittwoch, 5.12.12, 16:15-17:15, Hörsaal II, Albertstr. 23b
We analyze a constrained minimization problem for the Willmore energy. For a given parameter a>0 we consider smooth embeddings of the sphere into the unit ball with surface area \(a\). In this class we minimize the Willmore energy and investigate the dependence of the minimal energy value on the parameter a. (This is joint work with Stefan Müller, Bonn.)\n\n
Confined structures of least bending energy
Mittwoch, 5.12.12, 16:15-17:15, Hörsaal II, Albertstr. 23b
We analyze a constrained minimization problem for the Willmore energy. For a given parameter a>0 we consider smooth embeddings of the sphere into the unit ball with surface area \(a\). In this class we minimize the Willmore energy and investigate the dependence of the minimal energy value on the parameter a. (This is joint work with Stefan Müller, Bonn.)\n
Wadge-like reducibilities on arbitrary (quasi-)Polish spaces
Mittwoch, 5.12.12, 16:30-17:30, Raum 404, Eckerstr. 1
Donnerstag, 6.12.12, 17:00-18:00, Hörsaal II, Albertstr. 23b
Homology stability for special linear group and scissors congruence groups.
Freitag, 7.12.12, 10:00-11:00, Raum 404, Eckerstr. 1
The Scissors Congruence group - or pre-Bloch group - P(F),\nof a field F is a group presented by generators and relations which derive from the five-term functional equation of the dilogarithm.\n\nThe Bloch group is a subgroup of P(F) which, by a result of Suslin, is naturally a quotient of the indecomposable K3 of F, and this in turn is a quotient of the group H3(SL(2,F),Z). Up to some possible 2-torsion, the kernel of the map H3(SL(2,F),Z) to K3^ind(F) coincides with the kernel of the stabilization map from H3(SL(2,F),Z) to H3(SL(3,F),Z). We will describe how, for fields with valuations, lower bounds - and even exact computations - of this latter kernel can be expressed as direct sums of pre-Bloch groups of residue fields.
Montag, 10.12.12, 16:00-17:00, Raum 404, Eckerstr. 1
First order deformations in heterotic compactifications
Montag, 10.12.12, 16:00-17:00, Raum 404, Eckerstr. 1
Many beautiful geometric structures, such as Calabi-Yau (CY) manifolds and their moduli spaces, arise naturally in the context of string theory. In heterotic string theory a generalization of CY geometry is given by holomorphic vector bundles over CY spaces. This talk is concerned with more general heterotic geometries: vector bundles over complex but typically non-Kaehler manifolds. I will review this geometric structure and its origin in string theory and then focus on a characterization of the first order deformation space of these geometries.\n\n
Local results for Ricci flow on regions with curvature bounded from below
Dienstag, 11.12.12, 16:15-17:15, Raum 414, Eckerstr. 1
Donnerstag, 13.12.12, 17:00-18:00, Hörsaal II, Albertstr. 23b
L2-dbar-cohomology of singular complex spaces
Freitag, 14.12.12, 10:00-11:00, Raum 404, Eckerstr. 1
We will explain how one can use a resolution of singularities to understand the L2-Dolbeault-cohomology of a singular Hermitian complex space \(X\)\n(in the sense of finding a smooth model for the cohomology). The central tool is an L2-resolution for the Grauert-Riemenschneider canonical sheaf of \(X\).\nWe obtain particularly nice results if X is a Gorenstein space with canonical singularities, including an L2-representation of the cohomology of the structure sheaf.\nTo attack the more general case, we introduce a new kind of canonical sheaf, namely the canonical sheaf of square-integrable holomorphic\ntop-degree-forms with some (Dirichlet) boundary condition at the singular set of X. An L2-resolution for this sheaf allows to describe the L2-cohomology of arbitrary isolated singularities.
Geometric flows and special holonomy
Montag, 17.12.12, 16:15-17:15, Raum 404, Eckerstr. 1
Metrics with holonomy contained in G_2 on a 7-manifold are \ninduced by so-called positive 3-forms which are torsionfree, i.e. satisfy a \ncertain nonlinear 1st order PDE. I will discuss a parabolic flow on \npositive 3-forms whose stationary points are precisely given by the\ntorsionfree ones. This is joint work with F. Witt.\nIf time permits I will describe a generalization to a spinorial setting \n(joint with B. Ammann and F. Witt).
Witten's proof of positive mass theorem
Dienstag, 18.12.12, 16:15-17:15, Raum 404, Eckerstr. 1
I'll give a talk on Witten's proof of the positive mass theorem using spinors.
Cardinal Invariants and the P-Ideal Dichotomy
Mittwoch, 19.12.12, 16:30-17:30, Raum 404, Eckerstr. 1
Nichtstandardanalysis --- eine Anwendung auf interagierende Teilchensysteme, Filter und Semifilter
Donnerstag, 20.12.12, 16:15-17:15, Hörsaal II, Albertstr. 23b
Nichtstandardanalysis --- eine Anwendung auf interagierende Teilchensysteme
Donnerstag, 20.12.12, 16:15-17:15, Hörsaal II, Albertstr. 23b
Filter und Semifilter
Donnerstag, 20.12.12, 17:15-18:15, Hörsaal II, Albertstr. 23b
Pulling back differential forms
Freitag, 21.12.12, 10:00-11:00, Ort noch nicht bekannt
Donnerstag, 27.12.12, 17:00-18:00, Hörsaal II, Albertstr. 23b
Donnerstag, 3.1.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
Laminations of solutions in the Frenkel-Kontorova model with weak coupling
Montag, 7.1.13, 16:15-17:15, Raum 404, Eckerstr. 1
Perfect subsets of generalized Baire spaces and Banach-Mazur games
Mittwoch, 9.1.13, 16:30-17:30, Raum 404, Eckerstr. 1
Let \(\bkappa\) be an uncountable cardinal with \(\bkappa^{< \bkappa} = \bkappa\). We consider the generalized Baire space of functions \(f : \bkappa \bto \bkappa\) with basic open sets \(U_s = \b{f \bin \bkappa^\bkappa \bmid s \bsubseteq f \b}\) for \(s \bin {}^{< \bkappa} \bkappa\). A subset of \(\bkappa^\bkappa\) is perfect if it is the set of branches of a \(< \bkappa\)-closed subtree of \({}^{< \bkappa} \bkappa\) which splits above every node. We prove that after an inaccessible \(\blambda > \bkappa\) is collapsed to \(\bkappa^+\), every set \(A \bsubseteq \bkappa^\bkappa\) definable from ordinals and subsets of \(\bkappa\) either has size \(\bleq \bkappa\) or a perfect subset, and that the Banach-Mazur game for \(A\) is determined.
Donnerstag, 10.1.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
The Hele Shaw Flow and the Moduli of Holomorphic Discs
Freitag, 11.1.13, 10:00-11:00, Raum 404, Eckerstr. 1
The Hele-Shaw Flow is a model for describing the propagation of\nfluid in a cell consisting of two parallel places separated by a small\ngap. This model has been intensely studied for over a century, and is a\nparadigm for understanding more complicated systems such as the flow of\nwater in porous media, melting of ice and models of tumor growth.\n\nIn this talk I will discuss how this flow fits into the more general\nframework of "inverse potential theory" through the idea of complex\nmoments. I will then discuss joint work with David Witt Nystrom that\nconnects to the moduli space of holomorphic discs with boundary in a\ntotally real manifold. Using this we prove a number of short time\nexistence/uniqueness results for the flow, including the case of the Hele\nShaw flow with varying permeability starting from a smooth Jordan domain,\nand for the Hele Shaw flow starting from a single point.
Talk 1: A sharp quantitative isoperimetric inequality in higher codimension
Mittwoch, 16.1.13, 16:15-17:15, Hörsaal II, Albertstr. 23b
The Pila-Zannier proof of the Manin-Mumford conjecture
Mittwoch, 16.1.13, 16:30-17:30, Raum 404, Eckerstr. 1
Talk 2: A sharp quantitative isoperimetric inequality in higher codimension
Mittwoch, 16.1.13, 17:30-18:30, Hörsaal II, Albertstr. 23b
Donnerstag, 17.1.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
Modified surgery theory - Application to Bott manifolds
Freitag, 18.1.13, 10:00-11:00, Raum 404, Eckerstr. 1
One of the fundamental questions in geometric topology is the question whether two manifolds are diffeomorphic. Surgery theory translated that question as follows: Assuming they are simply connected it now reads: Are our manifolds h-cobordant? But for certain settings yet another transformation of our question is useful leading to modified surgery theory. The key idea here is to compare controlled bordism classes of manifolds.\n\nIn my talk I will explain how one can apply this theory to problems related to Bott manifolds. Bott manifolds are a very nice and explicite class of manifolds given as iterated CP^1-fiber bundles. They are of special interest since, conjecturally, they are diffeomorphic if and only if their cohomology rings are isomorphic.
Adiabatic limit of the Ray-Singer torsion
Montag, 21.1.13, 16:15-17:15, Raum 404, Eckerstr. 1
Amoeba of Sacks forcing without Cohen reals
Mittwoch, 23.1.13, 16:30-17:30, Raum 404, Eckerstr. 1
Limitations of the Euler method
Donnerstag, 24.1.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
Our goal is to calculate moments of stochastic differential equations (SDEs)\n(e.g. the stochastic Langevin equation, the stochastic Duffing-van der Pol\nequation, the stochastic Lotka-Volterra model, the Lewis-3/2-volatility\nmodel, the stochastic Lorenz equation). In the global Lipschitz case, the\napproximation method with optimal rate of convergence is the multilevel\nMonte Carlo Euler method. Most of the applied SDEs, however, have\nsuper-linearly growing coefficients. We show for this case that the\nmultilevel Monte Carlo Euler method does not even converge in general. The\nreason herefore is strong divergence of Euler's method. For this reason, we\nrecommend to be careful with Euler's method in applications. Instead, we\npropose a strongly converging numerical method with optimal rate of\nconvergence and provide its short Matlab code.\n
Canonical degree of curves on varieties of general type
Freitag, 25.1.13, 10:00-11:00, Raum 404, Eckerstr. 1
Analysis on crepant resolutions of Calabi-Yau orbifolds
Montag, 28.1.13, 16:15-17:15, Raum 404, Eckerstr. 1
A Calabi-Yau orbifold is locally modeled on C^n/G with G a finite subgroup of SU(n). If the singularity is isolated, then the crepant resolution (if it exists) is an ALE manifold, for which index-type results are well known. However, most of the time the singularity is not isolated, and for the corresponding crepant resolution there is no index theorem so far. In this talk, I present the first step towards obtaining such a result: I will introduce the class of iterated cone-edge singular manifolds and the corresponding quasi-asymptotically conical spaces (for which orbifolds and their crepant resolutions are an example), and build-up the general set-up for studying Fredholm properties of geometrical elliptic operators on these spaces. This is joint work with Rafe Mazzeo.\n
On rings of continuous p-adic valued functions
Dienstag, 29.1.13, 11:30-12:30, Raum 318, Eckerstr. 1
The Galois closure of ring extensions and a discriminant theorem of Stickelberger
Donnerstag, 31.1.13, 15:15-16:15, Raum 404, Eckerstr. 1
A classical result of algebraic number theory by L. Stickelberger states that the discriminant of a number field is an integer congruent to 0 or 1 modulo 4. We generalize this theorem to n-ic extensions of arbitrary base rings. To achieve this, we use the notion of Galois closures of arbitrary ring extensions, as introduced by M. Bhargava and M. Satriano, combined with new results from invariant theory generalizing the fundamental theorem of symmetric polynomials. In the end, we will also state a conjecture strengthening the given results.
Donnerstag, 31.1.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
Bogomolov-Sommese vanishing on log canonical pairs
Freitag, 1.2.13, 10:00-11:00, Raum 404, Eckerstr. 1
(infinity,n)-categories and Segal spaces
Freitag, 1.2.13, 11:00-12:00, Raum 404, Eckerstr. 1
Closed Geodesics on Open Manifolds with Convex Ends
Montag, 4.2.13, 16:15-17:15, Raum 404, Eckerstr. 1
Bray's proof of the Penrose conjecture
Dienstag, 5.2.13, 16:15-17:15, Raum 404, Eckerstr. 1
Donnerstag, 7.2.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
Freitag, 8.2.13, 10:00-11:00, tba
Tilting and mutations
Freitag, 8.2.13, 10:00-11:00, Raum 404, Eckerstr. 1
Cocycles of characteristic classes in smooth Deligne cohomology
Montag, 11.2.13, 10:15-11:15, Raum 318, Eckerstr. 1
In my talk I will start with an introduction to smooth Deligne cohomology and then present the main results of my diploma thesis.\nLet G be a compact connected Lie group with classifying space BG and let a be an integer cohomology class of even degree p on BG. Let F be a compact connected differentiable manifold with G-action satisfying further topological conditions, e.g. F is a Stiefel manifold. Suppose that a is the image under transgression in the universal G-principal bundle of a certain cohomology class on F. Given any G-principal bundle E on a compact manifold M, I will explain some of the main steps how to construct explicitly a natural class in Deligne cohomology which represents the a-characteristic class of the bundle E.\nAt the end I will dicuss some examples of characteristic classes which satisfy the assumptions made in the main theorem of my diploma thesis.
Becker-Gottlieb-Transfer for cohomology with twisted coefficients
Montag, 11.2.13, 14:15-15:15, Hörsaal II, Albertstr. 23b
This talk is about Gottlieb's construction of a transfer for a fibre bundle and how it can be adapted to cohomology with twisted coefficients. This is achieved by adapting the primary tool of the transfer, which is integration along the fibre, to twisted cohomology.
Special Kähler geometry
Montag, 11.2.13, 16:15-17:15, Raum 404, Eckerstr. 1
I will give an introduction to special Kähler structures and some of their aspects. A special Kähler structure is a connection on the tangent bundle of a Kähler manifold with a number of "special" properties. They appear naturally in the context of certain integrable systems and of moduli spaces of Calabi-Yau threefolds.
Eta-forms of families of manifolds
Donnerstag, 14.2.13, 10:15-11:15, Raum 404, Eckerstr. 1
In index theory of families of closed manifolds the exterior differential of the eta-form describes the difference between the analytic and the topological index of a Dirac operator. Under the assumption that the horizontal distribution is integrable the question in my diploma thesis is if the eta-form is closed and defines a cohomology class in de Rham cohomology. At the end I'll look at the special case of a bundle of tori.
Freitag, 15.2.13, 10:00-11:00, Raum 404, Eckerstr. 1
Spectral curves of harmonic maps
Dienstag, 19.2.13, 13:15-14:15, Raum 404, Eckerstr. 1
To each harmonic map from a complex one-dimensional torus to the special unitary group SU(2) (respectively the 3-sphere) one can associate a hyperelliptic Riemann surface, the so-called spectral curve. This construction, mainly due to Hitchin, allows one to study such maps essentially by algebro-geometric methods. Its drawback is that it cannot be applied to higher genus. However, Heller has recently carried out an analogous construction for an example of higher genus, Lawson's surface of genus two, for the first time. We sketch an important step in this construction, the abelianization of certain flat connections over Lawson's surface.\n
Freitag, 1.3.13, 09:15-10:15, Raum 404, Eckerstr. 1
Symplectic Constraints of Field Theories
Freitag, 1.3.13, 09:15-10:15, Raum 404, Eckerstr. 1
For field theories defined on a manifold with a boundary\nthere exists a canonical symplectic structure. This structure enables the constraints of a field theory to be categorised and interpreted geometrically. In particular, Yang-Mills theory, BF theory and Chern-Simons theory all satisfy a theorem which relates the properties of this structure to the form of their actions.\n
Log Terminal Singularities (joint work with A. Chiecchio)
Freitag, 8.3.13, 10:00-11:00, Raum 404, Eckerstr. 1
Inspired by the work of de Fernex and Hacon on singularities of normal varieties (2009), we define a new notion for Log Terminal singularities. In this context we prove that the relative canonical ring is finitely generated and that log terminal varieties are klt in the usual sense if and only if the anti-canonical ring is finitely generated. We deduce a relation to the Minimal Model Program and some interesting features on defect ideals.
Transitivität von Automorphismengruppen von Gizatullin-Flächen
Dienstag, 12.3.13, 10:00-11:00, Raum 404, Eckerstr. 1
Abstract siehe http://www.gk1821.uni-freiburg.de/events/vortrag-von-sergei-kovalenko-bochum
Transitivity of automorphism groups of Gizatullin surfaces
Dienstag, 12.3.13, 10:00-11:00, Raum 404, Eckerstr. 1
On singular symplectic complex spaces
Freitag, 15.3.13, 10:00-11:00, Raum 404, Eckerstr. 1
I start out presenting basic results in the deformation theory of singular symplectic complex spaces. Among others I explain how (and in what sense) it is possible to generalize the well-known local Torelli theorem for hyperkähler manifolds to a possibly singular setting. As a consequence one obtains that certain irreducible symplectic spaces satisfy the Fujiki relation. If time allows, I shall discuss applications of the latter fact.