Oberseminar Geometrie, Topologie und Analysis

H. Geiges, A. Lytchak, G. Marinescu, S. Sabatini

Sommersemester 2018

Freitag, 10:30-11:30, Seminarraum 2 (Raum 204)

6.4.18 BGHK Seminar in Köln

13.4.18 Jingyin Huang (MPI Bonn)
Uniform lattices acting on RAAG complexes

Abstract: It is a classical result by Bieberbach that uniform lattices acting on Euclidean spaces are virtually free abelian. On the other hand, uniform lattices acting on trees are virtually free. This motivates the study of commensurability classification of uniform lattices acting on RAAG complexes, which are cube complexes that "interpolate" between Euclidean spaces and trees. We show the tree times tree obstruction is the only obstruction for commmensurability of label-preserving lattices acting on RAAG complexes. Some connections of this problem with Haglund and Wise's work on special cube complexes will also be discussed.
27.4.18 Nina Lebedeva (Petersburg/Münster)
Synthetic property of metric spaces related to continuity of optimal transport

Abstract: We introduce a new type of metric comparison which is stronger then Alexandrov comparison. This comparison is closely related to the continuity of optimal transport between regular measures.
27.4.18 Joint Seminar on Complex Algebraic Geometry and Complex Analysis in Wuppertal

4.5.18 Alexandra Otiman (MPI Bonn)
Cohomology of Oeljeklaus-Toma manifolds

Abstract: Oeljeklaus-Toma manifolds are a higher-dimensional generalization of Inoue-Bombieri surfaces and were introduced by K. Oeljeklaus and M. Toma in 2005. They are quotients of Hs× Ct by discrete groups of affine transformations arising from a number field K and a particular choice of a subgroup of units U of K. They are commonly referred to as OT manifolds of type (s,t).
OT manifolds have been of particular interest for locally conformally Kähler (lcK) geometry since they do not admit Kähler metrics, but those of type (s,1) admit lcK metrics and for (s,t) in general, the existence of an lcK metric reduces to a number-theoretic condition.
In this talk, we compute their de Rham and twisted cohomology and derive several applications concerning the characterization of possible Lee classes for lcK metrics, the twisted cohomology class of lcK metrics and the low-degree Chern classes of complex vector bundles over OT manifolds.
BGHK Seminar in Bochum

22.6.18 Daniel Grieser (Oldenburg)
Geodesics on singular spaces

Abstract: The geodesics emanating from a point p in a Riemannian manifold together define the exponential map based at p. We consider the question whether there is an exponential map based at a singular point. We give an affirmative answer for special classes of singularities including conical and cuspidal singularities. However, the exponential map exhibits surprising properties in some cases, like not being injective in any neighborhood of p. Important tools in the study of this question are blow-ups, Hamiltonian systems with degenerate symplectic form and normally hyperbolic dynamical systems.
29.6.18 Martin Puchol (Paris Sud)
Variance of the volume of random real algebraic submanifolds

Abstract: The object of interest in this talk is the common zero set Zd of r independent random polynomials of degree d in the real n-dimensional projective space. We will study the asymptotics of the variance of its volume as the degree grows to infinity, and give some applications, such as asymptotic a.s. density. This study will be in fact carried out in the more general setting of real projective manifold endowed with growing tensor powers of a real ample line bundle.
6.7.18 Joint Seminar on Complex Algebraic Geometry and Complex Analysis in Köln

13.7.18 Megumi Harada (McMaster)
The cohomology of abelian Hessenberg varieties and the Stanley-Stembridge conjecture

H. Geiges, 5.4.02