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.