Bogomolov-Sommese vanishing on log canonical pairs
Friday, 1.2.13, 10:00-11:00, Raum 404, Eckerstr. 1
(infinity,n)-categories and Segal spaces
Friday, 1.2.13, 11:00-12:00, Raum 404, Eckerstr. 1
Closed Geodesics on Open Manifolds with Convex Ends
Monday, 4.2.13, 16:15-17:15, Raum 404, Eckerstr. 1
Bray's proof of the Penrose conjecture
Tuesday, 5.2.13, 16:15-17:15, Raum 404, Eckerstr. 1
Thursday, 7.2.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
Friday, 8.2.13, 10:00-11:00, tba
Tilting and mutations
Friday, 8.2.13, 10:00-11:00, Raum 404, Eckerstr. 1
Cocycles of characteristic classes in smooth Deligne cohomology
Monday, 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
Monday, 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
Monday, 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
Thursday, 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.
Friday, 15.2.13, 10:00-11:00, Raum 404, Eckerstr. 1
Spectral curves of harmonic maps
Tuesday, 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