Oberseminar Geometrie, Topologie und Analysis

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

Sommersemester 2015

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

10.4.15 Otto van Koert (Seoul National University, z.Zt. Augsburg)
Invariants of contact structures and Sasakian geometry

24.4.15 Xiaonan Ma (Paris 7)
Optimal convergence speed of Bergman metrics on symplectic manifolds

Abstract: A compact symplectic manifold endowed with a prequantum line bundle L can be embedded in the projective space by certain sections of high p-tensor powers of L. We show that the Fubini-Study metrics induced by these embeddings converge at speed rate 1/p2 to the symplectic form. This should give a generalization to the almost Kähler case of Donaldson's lower bounds of the Calabi functional and a symplectic "algebraic" notion of the Futaki invariant.
15.5.15 Michael Lennox Wong (EPFL)
Moduli spaces of irregular connections and their character varieties

Abstract: A holomorphic connection on a holomorphic vector bundle over a compact Riemann surface will yield a representation of the fundamental group by taking the monodromy representation at any base point, from which the connection can be recovered. If one allows the connection to have simple poles at a finite set of points, there is a straightforward generalization where one now takes the fundamental group of the punctured surface. After reviewing these facts, the main goal of this talk will be to explain how the Stokes phenomenon arises when one considers meromorphic connections with higher order poles. The corresponding space of monodromy data is known as a "wild" character variety, and if time and planning allow, we will provide the motivation for and discuss the computation of some geometric invariants of these varieties obtained in ongoing work with Tamás Hausel and Martin Mereb.
19.6.15 Masanori Adachi (Tokyo University of Science)
The Ohsawa-Sibony embedding and the Diederich-Fornaess index

Abstract: We would like to discuss a foliated version of Kodaira's embedding theorem, namely, we consider a compact manifold foliated by complex manifolds equipped with a positive leafwise holomorphic line bundle, and ask whether we can embed it in a complex projective space using leafwise holomorphic sections of high power of the bundle. Ohsawa and Sibony gave an affirmative answer, but their embedding map is only proved to be finitely differentiable to transversal direction. We therefore are led to investigate the balance among dynamics of the foliation, positivity of the bundle and transversal differentiability of the embedding map. In this talk, we will first exhibit examples showing that infinite differentiability is not promised in general, then explain our approach based on the Diederich-Fornaess index, which measures certain speed of possible contact approximations of the foliation, and report its recent progress.
26.6.15 Stephan Gareis
Fakultätsöffentliche Disputation

H. Geiges, 5.4.02