Programmdiskussion
Montag, 21.10.13, 16:15-17:15, Raum 404, Eckerstr. 1
Conformally flat cylinders without conjugate points
Montag, 4.11.13, 16:15-17:15, Raum 404, Eckerstr. 1
For surfaces without conjugate points, Eberhard Hopf's method leads to optimal rigidity results. The question arises of whether (a generalization of) the method is equally powerful in higher dimensions. We will investigate the case of conformally flat cylinders.
Trapped Reeb orbits do not imply periodic ones
Montag, 11.11.13, 16:15-17:15, Raum 404, Eckerstr. 1
Euler Structures on Fibre Bundles
Montag, 18.11.13, 16:15-17:15, Raum 404, Eckerstr. 1
Cones over metric measure spaces and the maximal diameter theorem
Montag, 25.11.13, 16:15-17:15, Raum 404, Eckerstr. 1
We briefly describe the definition of curvature-dimension bounds in the sense of Lott-Villani/Sturm (CD(K,N)) and recent results about Riemannian differential calculus for metric measure spaces. Then we present the following theorem: the cone over a metric measure space satisfies CD(KN,N-1) if and only if the underlying space satisfies CD(N-1,N). As consequence of this result and the Cheeger-Gigli-Gromoll splitting theorem we obtain a maximal diameter theorem in the context of metric measure spaces.
The Kähler-Einstein problem
Montag, 2.12.13, 16:15-17:15, Raum 404, Eckerstr. 1
This will be an overview of the Kähler-Einstein problem, including its very recent resolution in the positive case.
A universal eta-Invariant for G2-Structures
Montag, 9.12.13, 16:00-17:00, Raum 404, Eckerstr. 1
In this talk I will give a short introduction to the exceptional Lie-group G2. Then I will motivate G2-structure with G2-manifolds, i. e. Riemannian manifolds with holonomy group G2, that are an exceptional case in the classification of Berger and allegedly have applications in physics. On these G2-structures Crowley and Nordström defined the nu-invariant with values in Z/48Z, which I will explain. The mod 3 reduction of the nu-invariant is a G2-bordism invariant and has been interpreted as a universal eta-invariant in my thesis.
tba
Montag, 9.12.13, 16:15-17:15, Raum 404, Eckerstr. 1
Algebraic K-theory, eta-invariant and homology sphere
Montag, 16.12.13, 16:15-17:15, Raum 404, Eckerstr. 1
In this talk we will discuss how to use eta-invariant to find some geometric models for some algebraic K-groups.
Some simple singularity theory
Montag, 13.1.14, 16:15-17:15, Raum 404, Eckerstr. 1
Classifying superconformal field theories via chiral rings
Montag, 20.1.14, 16:15-17:15, Raum 404, Eckerstr. 1
I will introduce some of the main mathematical ideas behind N=2 superconformal field theory, using the N=2 minimal models as a concrete example, and explore some of their connections to geometry. \n\nTo illustrate these ideas I will focus on the so-called "chiral rings", which arise from basic Lie algebra representation theory plus ideas from quantum field theory. I show how the chiral rings relate to Calabi-Yau geometry, then I'll describe how chiral rings appear in Cecotti and Vafa's famous ADE singularity classification of a special subclass of N=2 minimal models (those with "space-time supersymmetry"), and we'll briefly reacquaint ourselves with some other prominent appearances the ADE pattern in maths and physics.\n\nFinally I'll present the chiral rings of the entire class of N=2 minimal models (when the extra assumption of space-time supersymmetry is dropped) and report on ongoing work with K. Wendland concerning a geometric classification of these theories.\n
tba
Montag, 27.1.14, 16:15-17:15, Raum 404, Eckerstr. 1
Complex multiplication on abelian varieties
Montag, 27.1.14, 16:15-17:15, Raum 404, Eckerstr. 1
tba
Montag, 3.2.14, 16:15-17:15, Raum 404, Eckerstr. 1
Eta-forms in family index theory
Montag, 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.
Vorstellung Masterarbeit
Montag, 10.2.14, 16:15-17:15, Raum 404, Eckerstr. 1
Bounded cohomology via partial differential equations
Montag, 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
Dienstag, 18.2.14, 10:15-11:15, Raum 404, Eckerstr. 1
Coarse topology of leaves of foliations
Freitag, 21.2.14, 10:15-11:15, Raum 404, Eckerstr. 1