tba
Monday, 3.2.14, 16:15-17:15, Raum 404, Eckerstr. 1
Eta-forms in family index theory
Monday, 3.2.14, 16:15-17:15, Raum 404, Eckerstr. 1
This talk will give a short introduction how the differential of the eta form gives the difference between the cohomological and the analytical index. Then we'll look at an example where the dimension of the kernel of the Dirac operator changes and see how this affects the eta-form.
Bad Wadge-like reducibilities on the Baire space and on arbitrary ultrametric Polish spaces
Wednesday, 5.2.14, 16:00-17:00, Raum 404, Eckerstr. 1
Weightless cohomology of algebraic varieties
Thursday, 6.2.14, 11:00-12:00, Raum 218, Eckerstr. 1
Using Morel's weight truncations in categories of mixed sheaves, we attach to any variety defined over complex numbers, over finite fields or even over a number field, a series of groups called the weightless cohomology groups . These lie between the usual cohomology and the intersection cohomology, have a natural ring structure, satisfy Kunneth, and are functorial for certain morphisms.\n The construction is motivic and naturally arises in the context of Shimura Varieties where they capture the cohomology of Reductive Borel Serre compactification. The construction also yields invariants of singularities associated with the combinatorics of the boundary divisors in any resolution.
Thursday, 6.2.14, 17:00-18:00, Hörsaal II, Albertstr. 23b
Motives of rigid analyic varieties over perfectoid fields
Friday, 7.2.14, 10:15-11:15, Raum 404, Eckerstr. 1
The aim of the talk is to outline the proof of the equivalence between the category of motives of rigid analytic varieties (defined by Ayoub adapting Voevodsky's construction) over a perfectoid field of mixed characteristic and over the associated (tilted) perfectoid field of equal characteristic. This can be considered as a motivic generalization of a theorem of Fontaine and Wintenberger regarding the isomorphism of the two absolute Galois groups. A main tool for constructing the equivalence is Scholze's theory of perfectoid spaces, which will also be briefly discussed.\n
Geometrisch-optische Illusionen und Riemannsche Geometrie
Friday, 7.2.14, 11:30-12:30, Raum 404, Eckerstr. 1
Vorstellung Masterarbeit
Monday, 10.2.14, 16:15-17:15, Raum 404, Eckerstr. 1
Bounded Hyperimaginaries
Wednesday, 12.2.14, 16:30-17:30, Raum 404, Eckerstr. 1
Thursday, 13.2.14, 17:00-18:00, Hörsaal II, Albertstr. 23b
Friday, 14.2.14, 10:15-11:15, Raum 404, Eckerstr. 1
Bounded cohomology via partial differential equations
Monday, 17.2.14, 10:15-11:15, Raum 404, Eckerstr. 1
By the van Est isomorphism, continuous cohomology of simple Lie groups vanishes in degree greater than the dimension of the associated symmetric space. Monod conjectured that a similar vanishing theorem should hold for continuous bounded cohomology. In this talk, we will present a new technique that employs partial differential equations in order to explicitly construct primitives in the continuous bounded cohomology of Lie groups. As an application, we prove Monod's conjecture for SL(2,R) in degree four and discuss perturbations of the Spence-Abel functional equation for the dilogarithm function. This is joint work with Tobias Hartnick.\n
The asymptotic geometry of the moduli space of Higgs bundles over a Riemann surface
Tuesday, 18.2.14, 10:15-11:15, Raum 404, Eckerstr. 1
Soulé-elements, p-adic periods & an explicit reciprocity law
Wednesday, 19.2.14, 14:15-15:15, Raum 404, Eckerstr. 1
Coarse topology of leaves of foliations
Friday, 21.2.14, 10:15-11:15, Raum 404, Eckerstr. 1
Intersection theory on singular varieties
Tuesday, 25.2.14, 10:15-11:15, Hörsaal II, Albertstr. 23b
We introduce some ideas from motivic cohomology into the study of singular varieties. Our approach is modeled on the intersection homology of Goresky-MacPherson; our goal is to intersect cycles on a stratified singular variety provided the cycles do not meet the strata too badly. We define "perverse" analogues of Chow groups and motivic cohomology. Properties include homotopy invariance, a localization theorem, and a splitting theorem. As a consequence we obtain pairings between certain "perverse" cycle groups on a singular variety.\n\n