COLLOQUIUM Mélanie Bertelson "Conformal symplectic structures in contact geometry"
Prof.Mélanie Bertelson(Université libre de Bruxelles)
René Baire (IMB)
Abstract : Contact geometry has become an important field of research through its close connection with symplectic geometry and also since the discovery by Eliashberg of the dichotomy tight versus overtwisted. Tight contact structures are rigid while overtwisted ones are flexible and abide an h-principle. Tight contact structures are more difficult to construct. This has lead to many very interesting developments over the years. Namely, in dimension three, Eliashberg and Thurston have shown how to obtain such structures from taut foliations. An attempt to adapt their construction to higher dimension makes use of the notion of conformal symplectic structures.
My plan is to review some elementary aspects of contact geometry, explain the notion of tightness, define conformal symplectic structures, describe the main ideas behind h-principles and explain the Eliashberg-Thurston theory mentioned above.