Polyfold Theory towards the Fukaya Category is a week-long summer school / workshop at UC Berkeley, June 12-16, 2017, which will discuss the polyfold foundations for a construction of the Fukaya category in general symplectic manifolds. Our goal is to enable participants to apply polyfold theory to new moduli spaces themselves ... and possibly to recruit and train contributors to a crowd-sourcing project of accessibly documenting the polyfold construction of (various flavours of) Fukaya categories.
This summer school is open to and appropriate for all graduate students and researchers who are interested in the topic and have (or are willing to lay) a significant part of the foundations listed in the Reading List. However, please don't be shy about applying if you are new to polyfold theory. We will offer an online reading-support-group prior to the summer school as well as afternoon discussion groups to go over the basic notions of polyfold theory. Our primary goal is to broaden, diversify, and strengthen the base of educated polyfold users.

Lecturers

Nate Bottman, IAS Princeton; Joel Fish, UMass Boston; Katrin Wehrheim, UC Berkeley;
"polyfold lab" graduate students: Ben Filippenko, Wolfgang Schmaltz, Zhengyi Zhou, all UC Berkeley;
more to be confirmed

Registration

Please fill out this form by May 20 to be eligible for housing. We are making funding decision on a rolling basis until available housing/budget are filled up.

Travel and accommodation info


Financial Support and General Accessibility

As part of the NSF Training Group in Geometry and Topology, we are able to fund US citizens and permanent residents that are ``young researchers''. However, we are also able to fund senior and/or non-US participants from smaller, more flexible, funds. More generally, we are fully committed to maximizing accessibility, so if you are interested in particpating, please let us know your needs and we will work out a solution.
To apply for funding, just fill out the registration form, which asks also for a short letter of reference from an advisor (or other person who can make suitable comments on the mathematical fit between you and the goal of this summer school).

Schedule

A detailed schedule will be provided in time .. here is the basic plan:
Mornings: lecture course going through polyfold theory at examples towards the Fukaya category.
Afternoons: workshop discussions on background and technical details; some specialized talks; time for group work on polyfold constructions .. or non-math activities (see below for suggestions).
On Monday afternoon we will invite all participants to give a 5 minute flash talk to let people know what (math and otherwise) they are interested in connecting on during the workshop.
The schedule on Friday afternoon will be informal to allow for flexible departures.
We will also offer at least one fireside chat on navigating math culture .. and contributing to it!
All events will take place in 1015 Evans hall (unless otherwise announced).

Reading List for preparation

We hope to build on the following background - and will organize an online reading group in the week(s) leading up to the summer school for those participants who have not (yet) seen most of this:

  • basic analysis of Floer theory at the level of sections 1-3 of Salamon's Lectures on Floer homology; other good sources for this are the textbooks by Audin-Damian or (parts of) McDuff-Salamon;

  • basic ideas of Fukaya categories at the level of section 2 of Auroux's ''Beginner's introduction to Fukaya categories"; other good sources for this are (small parts of) the books by Seidel, or Fukaya-Oh-Ohta-Ono.

  • basic ideas of Polyfold Theory, as surveyed in e.g. Polyfolds: A First and Second Look (by O.Fabert, J.Fish, R.Golovko, K.Wehrheim), or the original papers by Hofer-Wysocki-Zehnder cited therein;


  • Some suggestions for non-math activities

    • Hike in Tilden Park. Take the H-Line bus from outside of Evans ($1 fare, schedule here) to MSRI (at Grizzly Peak and Centennial). From there, explore the trails in Tilden, or head to the Tilden park Botanical garden. Here is a park trail map. Return by foot (~1 hour walk) or H-Line shuttle bus.

    • The H-line bus also runs to the UC Botanical garden and the Lawrence hall of science. Both are free for Berkeley students, small admission charge otherwise.

    • Further afield, but easily accessible by BART, is the Oakland Museum of California (Lake Merritt stop) and, of course, all of San Francisco.

    Contact info

    Questions? Contact Katrin Wehrheim or e-mail polyfoldsummer - at - gmail - dot - com.