Seminar – Topics in symplectic geometry (Dr. U. Fuchs)

WiSe 17/18


This seminar can serve as an introduction to contact geometry in dimension 3. Among the topics we will discuss are: existence of contact structures, tight/overtwisted dichotomy, open book decompositions, characteristic foliations, convex surfaces, transverse/Legendrian knots.

Ort und Zeit


Mittwoch 14 - 16 in INF 205 / SR 3

Literatur

John Etnyre - Introductory Lectures on Contact Geometry

Hansjörg Geiges - An Introduction to Contact Topology


Bitte bei MÜSLI anmelden


SoSe 17


We will discuss generating functions for Lagrangian submanifolds in cotangent bundles (as well as Legendrian submanifolds in 1-jet bundles) and explore their use in establishing rigidity phenomena for such submanifolds.

Vorträge


April 24 Introduction and generalities (Urs)
May 8 Special generating functions (Anna-Maria)
May 5 Existence of generating functions I (Irene)
May 22 Existence of generating functions II (Irene)
May 29 Uniqueness of generating functions is preserved under Hamiltonian isotopies (Matthias)
June 12 Uniqueness of generating functions for the zero section I (Urs)
June 19 Uniqueness of generating functions for the zero section II (Urs)
June 26 Correspondences and Reductions (Urs)
July 7 Lower bounds on Lagrangian intersection points via generating functions (Myeonggi)
July 10, Invariants of Lagrangian submanifolds via generating functions (Irene)


Literatur

Yasha Eliashberg and Misha Gromov - Lagrangian intersection theory: finite-dimensional approach.

François Laudenbach and Jean-Claude Sikorav - Persistance d'intersection avec la section nulle au cours d'une isotopie hamiltonienne dans un fibré cotangent.

Jean-Claude Sikorav - Problèmes d’intersection et de points fixes en géométrie hamiltonienne

David Théret - A complete proof of Viterbo's uniqueness theorem on generating functions.

Claude Viterbo - Generating functions, symplectic geometry, and applications.

Claude Viterbo - Symplectic topology as the geometry of generating functions.