Two weeks on Global Analysis

course: Extended Morse-Floer complexes in symplectic topology

speaker: Octav Cornea (Université de Montréal)

abstract: The Floer complex is probably the main tool in symplectic topology. Its definition parallels that of the Morse complex. In particular, it is a chain complex generated freely over the integers (or the integers mod 2) by the critical points of some (action) functional. Its dierential reflects the geometry of 0 and 1 dimensional moduli spaces of certain connecting orbits. These lectures will be focused on the following idea: by appropriately enlarging the coecient ring one can define an extended Morse complex whose geometry encodes algebraic higher-dimensional moduli spaces. I will explain how this construction can be applied in the Floer context and how it can be extended such as to take into account bubbling. I will also discuss some applications. These lectures are based on joint work with Jean-Francois Barraud and Francois Lalonde.

timetable:
Mon 14 Feb, 11:30 - 12:25, Sala Conferenze Centro De Giorgi
Tue 15 Feb, 11:30 - 12:25, Sala Conferenze Centro De Giorgi
Wed 16 Feb, 11:30 - 12:25, Sala Conferenze Centro De Giorgi
Thu 17 Feb, 11:30 - 12:25, Sala Conferenze Centro De Giorgi
Fri 18 Feb, 11:30 - 12:25, Sala Conferenze Centro De Giorgi
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