3:00 p.m., Monday (December 6, 2004)

Math Annex 1100

Helmut Hofer
Courant Institute
New York University

Quantitative Symplectic Geometry

This will be a very elementary talk about a very non-elementary subject. The beautiful fact is that problems and results are easy to understand, while the proofs usually have to rely on heavy duty machinery like symplectic field theory. Quantitative symplectic geometry is concerned with the ``size" of a symplectic space. A good starting point is already the consideration of open sets in a linear symplectic space. Since about 20 years, we know that there is a fascinating world of invariants going beyond volume measurements. The resulting theory is the theory of symplectic capacities. It is the main goal of these lectures to show that this theory is rather at its beginnings and far from being mature. In fact most of the key questions seem to be open.

Refreshments will be served at 2:45 p.m. in the Faculty Lounge, Math Annex (Room 1115).

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