Seminar

Starting 10am sharp, and continuing last weeks' discussion,

* Katrin Wehrheim will explain the abstract form of 'local models' in polyfold theory, which generalize 'smooth functions on open subsets of R^n'. In applications, these models arise from scale-smoothness of reparametrization actions, and reframing gluing analysis as Fredholm property for a function on a retract.

* Dusa McDuff will explain the construction of a special (finite dimensional "Kuranishi") reduction of any polyfold Fredholm section - thus reducing the VMC construction in symplectic topology to the construction of an Euler class for a smooth section of an orbibundle (with noncompact base).

A finite dimensional version of this construction extracts a particularly well organized orbifold atlas from any etale proper groupoid.

general logistics:

In future meetings, this seminar will concentrate on the polyfold technology developed by Hofer-Wysocki-Zehnder - assuming basic background (e.g. Polyfolds: A First and Second Look) or acceptance of a large black box.

In particular, our 'polyfold lab consulting service' will aim to turn dream proofs involving compact J-curve moduli spaces into rigorous polyfold proofs. Please contact katrin@math.berkeley.edu if you have dream proofs to offer.