Webrelaunch 2020

Symplectic embeddings and plane curves singularities

  • Speaker: Dr. Emmanuel Opshtein, Université de Strasbourg
  • Place: Maschinenbau, Oberer Hörsaal (10.91, R 222)
  • Time: 24.5.2013, 15:30 - 16:30
  • Invited by: Prof. Dr. Enrico Leuzinger (Geometry-Day II)


The problem of symplectic embeddings can be described in the following way : fix a reference domain D, equiped with a symplectic structure, and try to probe symplectic manifolds by asking whether and how D can embed into them. The theory is well-developped when the source domain is an ellipsoid in C², and the symplectic manifolds are 4-dimensional, of so-called non-simple SW type. Although these manifolds are rather special, there are intersting examples, such as the projective space and all its blow-ups ...

The aim of the talk will be to explain a very strong relation between the problem of symplectic embeddings of some special domains (like ellipsoids), and the realization of plane singularities by low degree curves. The main point will be to explain that symplectic geometry can give some hints on a purely algebraic-geometry problem.