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A polyfold lab report

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SYGW05 - Symplectic geometry - celebrating the work of Simon Donaldson

Co-authors: Ben Filippenko (UC Berkeley), Wolfgang Schmaltz (UC Berkeley), Zhengyi Zhou (UC Berkeley), Joel Fish (UMass Boston), Peter Albers (Uni Heidelberg)

I will survey various results on applications and extensions of Hofer-Wysocki-Zehnder's polyfold theory: – fiber products of polyfold Fredholm sections – equivariant transversality – existence and obstructions – equivariant fundamental class – coherent perturbations – Gromov-Witten axioms – two polyfold proofs of the Arnold conjecture These are joint with or due to Peter Albers, Ben Filippenko, Joel Fish, Wolfgang Schmaltz, and Zhengyi Zhou.

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