Schriftzug: Fachbereich Mathematik 
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Berlin-Hamburg-Seminar am 9.12.2016

Sylvain Courte (Grenoble)  Generating functions and sheaves for links in R3

To a (generic) one-parameter family of functions (fx) on a manifold M we associate the graph of all critical values : this is the front projection of a Legendrian link L in R3 and (fx) is called a generating function for L. Which Legendrian links admit a generating function? How many up to equivalence? To deal with such questions it is natural to associate to a generating function a sheaf on R2 microsupported on the Legendrian. We will discuss to what extent this is a bijective correspondence. This is joint work (in progress) with Vivek Shende.

Umberto Hryniewicz (UF Rio de Janeiro)  Genus zero global surfaces of section

In this talk we will discuss the problem of constructing genus zero global surfaces of section for 3-dimensional Reeb flows, with prescribed binding orbits. We focus on the case of SO(3), and state a theorem which generalizes the classical result of Birkhoff, asserting that Birkhoff annuli are global surfaces of section of geodesic flows of positively curved metrics on the 2-sphere. We provide applications to the planar circular restricted three-body problem. Then we will address the case of more general contact 3-manifolds. This is joint work with Pedro Salomão and Kris Wysocki.



 
  Seitenanfang  Impressum 2016-11-28, Janko Latschev