Oberseminar Geometrie, Topologie und Analysis

Oberseminar Geometrie, Topologie und Analysis

H. Geiges, G. Marinescu, S. Sabatini, D. V. Vu

Wintersemester 2022/23

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

28.10.22 Naohiko Kasuya (Hokkaido)
On the contact boundary of a strongly pseudoconcave surface

Abstract: As is well known, the boundary structure of a strongly pseudoconvex surface is very restrictive. For example, the contact structure must be Stein fillable due to the result of Bogomolov and De Oliveira. By contrast, strongly pseudoconcave boundaries have some flexibility. In this talk we show that they are not restrictive at all, in the sense of contact structures. Namely, we prove that any closed co-oriented contact 3-manifold can be realized as the boundary of a strongly pseudoconcave surface. This is joint work with Daniele Zuddas (Trieste).

25.11.22 Eva Miranda (UPC Barcelona & Köln)
Two sides of a mirror

Abstract: Etnyre and Ghrist have unveiled a mirror between contact geometry and fluid dynamics reflecting Reeb vector fields as Beltrami vector fields. I'll present several applications of this mirror, including the detection of escape trajectories (for which I'll need to extend the mirror to a singular set-up).This talk is based on joint works (some of them ongoing) with Robert Cardona, Josep Fontana, Cédric Oms, and Daniel Peralta-Salas.

H. Geiges, 2.4.22


28.10.22	Naohiko Kasuya (Hokkaido) On the contact boundary of a strongly pseudoconcave surface Abstract: As is well known, the boundary structure of a strongly pseudoconvex surface is very restrictive. For example, the contact structure must be Stein fillable due to the result of Bogomolov and De Oliveira. By contrast, strongly pseudoconcave boundaries have some flexibility. In this talk we show that they are not restrictive at all, in the sense of contact structures. Namely, we prove that any closed co-oriented contact 3-manifold can be realized as the boundary of a strongly pseudoconcave surface. This is joint work with Daniele Zuddas (Trieste).
25.11.22	Eva Miranda (UPC Barcelona & Köln) Two sides of a mirror Abstract: Etnyre and Ghrist have unveiled a mirror between contact geometry and fluid dynamics reflecting Reeb vector fields as Beltrami vector fields. I'll present several applications of this mirror, including the detection of escape trajectories (for which I'll need to extend the mirror to a singular set-up).This talk is based on joint works (some of them ongoing) with Robert Cardona, Josep Fontana, Cédric Oms, and Daniel Peralta-Salas.