Talks by Erman Cineli (Jussieu) and Georgios Dimitroglou Rizell (Uppsala).

Participation is free of charge.

Registration until April 5th, 2024, by email to lu@mathi.uni-heidelberg.de

Program:

Lunch: 12:00 - 13:30 Common Room on the 5th floor of INF 205

13:30 Erman Cineli (Jussieu):  Invariant Sets and Hyperbolic Periodic Orbits of Reeb Flows

Abstract: In this talk we will discuss the impact of hyperbolic (or, more generally, isolated as an invariant set) closed Reeb orbits on the global dynamics of Reeb flows on the standard contact sphere. We will discuss extensions of two results previously known for Hamiltonian diffeomorphisms to the Reeb setting. The first one asserts that, under a very mild dynamical convexity type assumption, the presence of one hyperbolic closed orbit implies the existence of infinitely many simple closed Reeb orbits. The second result is a higher-dimensional Reeb analogue of the Le Calvez-Yoccoz theorem, asserting that no closed orbit of a non-degenerate dynamically convex Reeb pseudo-rotation is isolated as an invariant set. The talk is based on a joint work with Viktor Ginzburg, Basak Gurel and Marco Mazzucchelli.

14:30  Coffee break

15:30 Georgios Dimitroglou Rizell (Uppsala): Rational convex surfaces with only hyperbolic complex tangencies

Abstract: We combine techniques from symplectic topology and complex analysis to construct examples of rationally convex surfaces of genus g that are totally real outside of a number 2g-2 hyperbolic tangencies. We construct fillable unknotted examples in the standard unit contact sphere in C2, as well as non-fillable and knotted examples inside C2. This is joint work with Mark Lawrence.

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