Tentative Information

Videos

Schedule of talks

Week of July 6 - 10

Monday Tuesday Wednesday Thursday Friday
9:30 - 10:30 McDuff Biran Fish 3/3 Viterbo Bottman
11:00 - 12:00 Wendl 1/3 Wendl 2/3 Eliashberg Wendl 3/3 Hutchings 3/3
12:30 - 2:30 Banquet
2:00 - 3:00 Wehrheim 1/2 Fish 2/3 Bottman (disc.)[1] Wehrheim 2/2 Nelson
3:30 - 4:30 Fish 1/3 Wendl (disc.) Hutchings 1/3 [2] Hutchings 2/3 Hutchings (disc.)
5:00 - 6:00 Office Hours 1 Office Hours 2

[1] Bottman discussion is 2:30pm - 3:30pm
[2] Hutchings lecture is 4:00pm - 5:00pm


Week of July 13 - 17

Monday Tuesday Wednesday Thursday Friday
9:30 - 10:30 Hofer 1/4 free day Hofer 2/4 Hofer 3/4 Hofer 4/4
11:00 - 12:00 Solomon free day Ekholm 2/3 Ekholm 3/3 Gardiner
12:30 - 2:30 free day Banquet
2:00 - 3:00 Bottman (disc.) free day Bourgeois Smith Abouzaid (disc.)
3:30 - 4:30 Ekholm 1/3 free day Abouzaid 2/3 Ekholm (disc.) Hofer (disc.)
5:00 - 6:00 Abouzaid 1/3 free day Hofer (with alcohol) Abouzaid 3/3

Mini-courses

Wendl (3 lectures): Classical transversality methods in SFT. For the purposes of this minicourse, a transversality result is called "classical" if it is of the form, "for a certain class of (domain-independent) almost complex structures J, the moduli space of J-holomorphic curves of a certain type is smooth and has the correct dimension." I will discuss results of this kind for finite-energy punctured J-holomorphic curves in symplectic cobordisms, i.e. the objects that are meant to be counted in Symplectic Field Theory. The focus on classical methods means that we exclude a variety of fancier notions such as domain-dependent/inhomogeneous/multivalued/abstract perturbations, thus it is in the nature of things that classical methods will not always suffice for a given application. But classical methods are generally what you should try first, because when they do work, they'll often make your life easier and reveal geometric information that can be harder to access in more abstract approaches.

Wehrheim/Fish/Hofer (9 lectures): Polyfolds and the construction of Symplectic Field Theory. (mini-course page) Polyfold theory provides a language and a large body of results in an area, which is a mixture of a generalized differential geometry, nonlinear functional analysis, and category theory. It includes a very general concept of a Fredholm section accompanied by Sard-Smale type transversality theory over the rational numbers, i.e. perturbing through rationally weighted multi-sections. As such, it is a powerful tool to address complicated transversality issues as they arise in constructing compact moduli spaces in symplectic geometry. In the first week, Fish and Wehrheim will introduce the analytic foundations of polyfold theory, including the notions of sc-calculus, retracts, M-polyfolds, strong bundles, Fredholm sections and regularization theorems. In the second week, Hofer will build on these foundations, aiming to construct the moduli spaces needed for general Symplectic Field Theory.

Hutchings (3 lectures): Obstruction Bundle Gluing. Obstruction bundle gluing is a method of calculating the number of ways of gluing certain configurations in which transversality fails, but not too badly. We will introduce this technique and show how it works in simple examples from Morse theory, contact homology, and embedded contact homology. (There might not be enough time to cover all of these examples.)

Ekholm (3 lectures): Knot contact homology. We define knot contact homology as the Legendrian differential graded algebra of the unit conormal lift of a knot and show how to compute it in terms of flow trees. Next, we show how to relate knot contact homology to a version of string topology. We conclude the mini course with how knot contact homology is related to the physical theories, Chern-Simons theory and topological string theory. Throughout we will use the 3-sphere as a guiding example.

Abouzaid (3 lectures): Lagrangian Floer cohomology in families. We will begin with a brief overview of Lagrangian Floer cohomology, in a setting designed to minimise technical difficulties (i.e. no bubbling). Then we will ponder the question of what happens to Floer theory when we vary Lagrangians in families, which we will not require to be Hamiltonian. We will see rigid analytic spaces naturally arise from such families; these spaces are the analogue of complex analytic manifolds over the Novikov field. In order to be faithful to the theme of the conference, we will end by constructing lots of moduli spaces in order to see that Floer complexes give rise to analytic coherent sheaves. In preparation, for the course, reading arXiv:1404.2659 is recommended, while reading arXiv:1408.6794 is definitely not recommended. A revised version of the second reference is in preparation, and should be available by the beginning of the summer school.

Abstracts:

Monday July 6

Tuesday July 7

Wendnesday July 8

Thursday July 9

Friday July 10

Monday July 13

Tuesday July 14

Free Day

Wednesday July 15

Thursday July 16

Friday July 17