2015 Summer School on Moduli Problems in Symplectic Geometry

6 juil. 2015, 08:30 → 17 juil. 2015, 18:00 Europe/Paris

Marilyn and James Simons Conference Center (IHES)

Organized as part of the IHÉS Lectures, this Summer School aims to provide PhD students, post-docs, and young researchers with an overview of recent developments in the theory of moduli spaces of pseudoholomorphic curves in symplectic and contact geometry.

Moduli spaces of pseudoholomorphic curves arise as the zero set of a Fredholm section of a suitable bundle. Provided this section can be appropriately perturbed, these moduli spaces yield powerful contact and symplectic invariants such as Gromov-Witten theory, contact homology, symplectic homology, and Symplectic Field Theory. Constructions and applications of these invariants will be addressed in detail during the workshop. There are two main perturbative techniques, geometric and functional analytic.

The geometric perturbation methods are powerful for applications and practical from a computational point of view but typically require many restrictive assumptions and fail to generalize broadly. We will introduce researchers to the polyfold machinery of Hofer, Wysocki, and Zehnder, a new analytic framework designed to resolve the issue of transversality systematically. As computations are integral in applications of the aforementioned invariants, we will also explore how geometric perturbation schemes can be incorporated into the polyfold package.

We will supplement 7 mini courses with moderated discussions and related talks by senior faculty on current and future directions for the field.

Confirmed speakers:

M. Abouzaid, Columbia University *
P. Biran, ETH Zürich
N. Bottman, Massachusetts Institute of Technology
F. Bourgeois, Université Paris-Sud Orsay
D. Cristofaro-Gardiner, Harvard University
T. Ekholm, Uppsala University *
Y. Eliashberg, Stanford
J. Fish, Institute for Advanced Study *
H. Hofer, Institute for Advanced Study *
M. Hutchings, UC Berkeley *
D. McDuff, Barnard College, Columbia University
J. Nelson, Columbia University and the Institute for Advanced Study
I. Smith, University of Cambridge
J. Solomon, Hebrew University
C. Viterbo, Ecole Normale Supérieure
K. Wehrheim, UC Berkeley *
C. Wendl, University College London *

* Mini course speakers

Organizing Committee

Chair: J. Nelson (Columbia University and the Institute for Advanced Study)
D. Cristofaro-Gardiner (Harvard University)
J. Fish (Institute for Advanced Study and UMass Boston)

Scientific Advisory Committee

H. Hofer (Institute for Advanced Study)
M. Hutchings (UC Berkeley)
D. McDuff (Barnard College, Columbia University)

With the support of La Société Générale

 

Itinerary swinning pool and moving club itinerary.pdf

Local Map Access LocalMapAccess.pdf

Places To Eat PlacesToEat.pdf

Poster IHES_Poster_11.pdf

lundi 6 juillet

1 Registration and welcome coffee

2 Dusa McDUFF

Introduction to Regularization Problems

3 Chris WENDL

Classical transversality methods in SFT (1/3)

12:00 Lunch Break

4 Katrin WEHRHEIM

Introduction to Polyfold Regularization (1/2)

15:00 Coffee break

5 Joel FISH

sc-Banach spaces and the sc-calculus (1/3)

17:00 Office Hours 1

mardi 7 juillet

09:00 Coffee

6 Paul BIRAN

Lagrangian Cobordisms, Dehn-twists and Real Algebraic Geometry

7 Chris WENDL

Classical transversality methods in SFT (2/3)

12:00 Lunch Break

8 Joel FISH

The rise of sc-retracts (2/3)

15:00 Coffee break

9 Chris WENDL

Discussion

17:00 Office Hours 2

mercredi 8 juillet

09:00 Coffee….

10 Joel FISH

Boundary, corners, strong bundles, and implicit function theorems (3/3)

11 Yakov ELIASHBERG

Midsummer Bures Dreams

12:00 Buffet Lunch at IHES

12 Nathaniel BOTTMAN

Discussion

15:30 Coffee break

13 Michael HUTCHINGS

Obstruction Bundle Gluing (1/3)

jeudi 9 juillet

09:00 Coffee….

14 Claude VITERBO

On properties of filling of contact manifolds (joint work with A. Oancea)

15 Chris WENDL

Classical transversality methods in SFT (3/3)

12:00 Lunch Break

16 Katrin WEHRHEIM

Regularization theorem for Fredholm sections of M-polyfold bundles (2/2)

15:00 Coffee break

17 Michael HUTCHINGS

Obstruction Bundle Gluing (2/3)

vendredi 10 juillet

09:00 Coffee….

18 Nathaniel BOTTMAN

Fredholm theory and Deligne-Mumford spaces for witch balls

19 Michael HUTCHINGS

Obstruction Bundle Gluing (3/3)

12:00 Lunch Break

20 Joanna NELSON

An Integral lift of contact homology

15:00 Coffee break

21 Michael HUTCHINGS

Discussion

lundi 13 juillet

09:00 Coffee…..

22 Helmut HOFER

Polyfolds and the construction of Symplectic Field Theory (1/4)

23 Jake SOLOMON

Holomorphic disks and special Lagrangians

12:00 Lunch Break

24 Helmut HOFER

Discussion

15:00 Coffee break

25 Tobias EKHOLM

Introduction to knot contact homology (1/3)

26 Mohammed ABOUZAID

Lagrangian Floer cohomology in families (1/3)

mercredi 15 juillet

09:00 Coffee….

27 Helmut HOFER

Polyfolds and the construction of Symplectic Field Theory (2/4)

28 Tobias EKHOLM

Knot contact homology and string topology (2/3)

12:00 Buffet Lunch at IHES

29 Frédéric BOURGEOIS

A symplectic invariant for contact manifolds

15:30 Coffee break

30 Mohammed ABOUZAID

Lagrangian Floer cohomology in families (2/3)

jeudi 16 juillet

09:00 Coffee….

31 Helmut HOFER

Polyfolds and the construction of Symplectic Field Theory (3/4)

32 Tobias EKHOLM

Knot contact homology, Chern-Simons theory, and topological string (3/3)

12:00 Lunch Break

33 Ivan SMITH

A symplectic Khovanov Puzzlebook

15:00 Coffee break

34 Tobias EKHOLM

Discussion

35 Mohammed ABOUZAID

Lagrangian Floer cohomology in families (3/3)

vendredi 17 juillet

09:00 Coffee….

36 Helmut HOFER

Polyfolds and the construction of Symplectic Field Theory (4/4)

37 Daniel CRISTOFARO-GARDINER

Symplectic embeddings of products

12:00 Lunch Break

38 Mohammed ABOUZAID

Discussion

15:00 Coffee break

39 Helmut HOFER

Discussion