TBA
Friday, 13.5.11, 10:15-11:15, Raum 404, Eckerstr. 1
TBA
Friday, 13.5.11, 11:15-12:15, Raum 127, Eckerstr. 1
On the geometry of strongly moving curves
Monday, 16.5.11, 09:00-10:00, Raum 125, Eckerstr. 1
Bridgeland stability conditions on threefolds and birational geometry
Friday, 20.5.11, 10:15-11:15, Raum 404, Eckerstr. 1
I will explain a conjectural construction of Bridgeland stability conditions on derived category of smooth projective threefolds. It is based on a a conjectural Bogomolov-Gieseker type inequality for the Chern character of "tilt-stable" complexes. In this talk, I will present evidence for the conjecture, as well as implications of the conjecture\nto the birational geometry of threefolds. In particular, it implies a weaker version of Fujita's conjecture.
Central Extensions of Linear Algebraic Groups, K-Theory and Homotopy Theory
Friday, 27.5.11, 10:00-11:00, Raum 404, Eckerstr. 1
In classical covering space theory we have an isomorphism of the fundamental group with the fibre of the universal cover over the basepoint. Covering spaces of topological groups are group extensions, but not every group extension is a covering space. \n\nPerfect groups admit a universal central extension and the kernel of this extension is also called fundamental group. For simply connected Chevalley-groups over a perfect field, this fundamental group, classically called second unstable K-Theory, is exactly the fundamental group of a simplicial resolution. A lot of examples will be given by explicit matrices in the special linear group.
Der Vortrag wird doch nicht stattfinden
Friday, 24.6.11, 10:15-11:15, Raum 404, Eckerstr. 1
Beschränkte Familien kohärenter Garben auf Kähler-Mannigfaltigkeiten
Friday, 1.7.11, 10:00-11:00, Raum 404, Eckerstr. 1
Lagrangian fibrations on hyperkähler manifolds
Friday, 8.7.11, 10:00-11:00, Raum 404, Eckerstr. 1
Hyperkähler (also called irreducible holomorphic symplectic) manifolds form an important class of manifolds with trivial canonical bundle. One fundamental aspect of their structure theory is the question whether a given hyperkähler manifold admits a Lagrangian fibration. I\nwill report on a joint project with Christian Lehn and Sönke Rollenske investigating the following question of Beauville: if a hyperkähler manifold contains a complex torus T as a Lagrangian submanifold, does it\nadmit a (meromorphic) Lagrangian fibration with fibre T ?
TBA
Friday, 8.7.11, 10:15-11:15, Raum 404, Eckerstr. 1
Sharp bounds on the denominators of the moduli part in the canonical bundle formula
Friday, 15.7.11, 10:00-11:00, Raum 404, Eckerstr. 1
The canonical bundle formula for a fibration f from (X,B)\nto Y consists in writing KX+B as the pullback of a sum of\nQ-divisors on Y, more precisely KX+B is the pullback of KY+D+M where KY is the canonical divisor, D contains some informations on the singular fibres and M is called moduli part.\n\nIt has been conjectured by Prokhorov and Shokurov that if\nthe fibres of f are curves then 12rM is base point free, where r is the Cartier index of the fibre. The conjecture in particular implies that 12rM has integer coefficients.\nIn this talk we will give a counterexample to the conjecture and we will give a sharp bound depending on r for the integer m such that mM has integer coefficients.
TBA
Friday, 22.7.11, 10:00-11:00, Raum 404, Eckerstr. 1
Ein Vergleich lokal analytischer Gruppenkohomologie mit Lie algebren Kohomologie für p-adische Lie Gruppen
Wednesday, 27.7.11, 14:00-15:00, Raum 404, Eckerstr. 1
Calculating the arithmetic volume of certain Shimura varieties using Borcherds theory.
Friday, 29.7.11, 10:00-11:00, Raum 404, Eckerstr. 1
The talk will be about the verification of parts of Kudla's\nconjectures on arithmetic theta functions, in particular of\ntheir relation to derivatives of Eisenstein series in\narbitrary dimensions. This approach uses an extended Arakelov theory, the theory of Borcherds products, and a functorial theory of integral canonical models of toroidal compactifications of Shimura varieties. Kudla's conjectures arose to conceptually understand the mechanism in Gross- and Zagier's approach to the Birch and Swinnerton-Dyer conjecture.