# RTG workshop program

Main lecturers: NB = Nate Bottman, JF = Joel Fish, KW = Katrin Wehrheim

## Contents

## Monday

9 Welcome & Logistics

9:15-10:15
lecture 1: *Overview of Fukaya category constructions* (KW)

10:15-10:30 discussion

coffee break

11-12
lecture 2: *The polyfolds, bundles, and sections relevant to Fukaya category - as topological objects* (KW)

12-12:30 discussion

lunch break

2-3:30 1-5 minute flash talks by all participants

coffee break

4-6 tutorial: scale calculus problems, see 2.2, 4.1-2 of [FFGW]; "warm-up" portion of problems on Deligne-Mumford spaces - with Catherine Cannizzo, Jeff Hicks, Jan-David Salchow

4-6 working groups on TBD / wiki-hackathon

6 pizza mix & mingle

## Tuesday

9-9:15 summaries of afternoon discussions

9:15-10:15 lecture 3: Deligne-Mumford space (NB)

10:15-10:30 discussion

coffee break

11-12
lecture 4: *Smooth structures for nonsingular parts of domains - featuring scale calculus* (JF)

12-12:30 discussion

lunch break

2-3 Kai Zehmisch on *Polyfolds and the Weinstein conjecture*

coffee break

3:30-5:30 tutorial: problems on retractions and M-polyfolds, see 2.3 and 5.1 in [FFGW] - with Ben Filippenko, Zhengyi Zhou optionally, try "further fun" portion of problems on Deligne-Mumford spaces (and question Nate about it ;-)

3:30-5:30 working groups on TBD / wiki-hackathon

5:30 snacks & panel discussion on *navigating math culture .. and contributing to it!* (Hiro Tanaka, JF, KW)

## Wednesday

9-9:15 summaries of afternoon discussions

9:15-10:15
lecture 5: *Smooth structures near nodes and Floer breaking - featuring retractions* (JF)

quick coffee break

10:30-11:30
lecture 6: *sc-Fredholm property of Cauchy-Riemann section in M-polyfold settings* (JF)

11:30-11:45 discussion

12- 1 Wolfgang Schmaltz on *Gromov-Witten axioms for polyfold construction*

lunch and free afternoon

## Thursday

9-9:30 Q&A (particularly on lectures 5, 6)

9:30-10:30
lecture 7: *Smooth structures near curves involving Morse flow lines* (KW)

10:30-10:45 discussion

coffee break

11:15-12:15 lecture 8: Global Polyfold Fredholm setup (how to patch it all together and deal with isotropy) (NB)

12:15-12:30 discussion

lunch break

2-3 Zhengyi Zhou on *Morse-Bott approach to invariance*

3-3:30 discussion of invariance

coffee break

4-6 tutorial: problems on Fredholm sections of polyfold bundles, perturbations, and implicit function theorems, see 2.1 and 6.1-3 in [FFGW] - with Wolfgang Schmaltz, and TBD

4-6 working group on invariance / wiki-hackathon

6 Cheeseboard pizza wrap-up mingle

## Friday

9-9:15 summaries of afternoon discussions

9:15-10:15
lecture 9: *Fiber products and coherent perturbations - featuring compactness controls by auxiliary norms* (Ben Filippenko)

10:15-10:30 discussion

coffee break

11-12
lecture 10: *Wrap-up of construction and Wish list of future constructions via polyfolds: invariance, homotopy units, bounding cochains... and more?* (NB)

12-12:30 discussion

lunch break

2-5 working groups on TBD / wiki-hackathon