Notes from Kylerec 2018

All notes are courtesy of Cédric De Groote! You can either view them:

  • In two parts (including notes from the West Coast Pre-Workshop):
  • Lecture-by-lecture. All the titles and speakers are listed below. All talks were meant to be an hour with the exceptions of Talks 3 and 4, which were meant to be half an hour each. The West Coast Pre-Workshop notes are not included here, but feel free to click the link above, or also check out the East Coast version.:
    • Day 1
      • Talk_1: Introduction and overview – Kyler Siegel
      • Talk_2: Morse theory and Floer theory – Yuan Yao
      • Talk_3: Gradings in Lagrangian Floer theory – Greg Parker
      • Talk_4: Signs in Lagrangian Floer theory – Laurent Côté
      • Talk_5: Symplectic cohomology and the Viterbo Theorem – Dahye Cho
    • Day 2
      • Talk_6: Spectral sequences – Ipsita Datta
      • Talk_7: Local systems – Daniel Vitek
      • Talk_8: Homology equivalence of nearby Lagrangians – Cédric De Groote
      • Talk_9: The \pi_1-isomorphism – Austin Christian
      • Discussion_Day_2
    • Day 3
      • Talk_10: Maslov = 0 – Thomas Kragh
      • Talk_11: (Wrapped) Fukaya categories – Sahana Vasudevan
    • Day 4
      • Talk_12: A_\infty algebras and categories – Maxim Jeffs
      • Talk_13: Hochschild (co)homology and the OC and CO maps – Abi Ward
      • Talk_14: Results on wrapped Fukaya categories – Semon Rezchikov
      • Talk_15: Generation and split-generation – Tim Large
      • Discussion_Day_4
    • Day 5
      • Talk_16: Homotopy equivalence of nearby Lagrangians with vanishing Maslov class – Alex Zhang
      • Talk_17: Exact Lagrangians in the plumbings of two cotangent bundles – Orsola Capovilla-Searle
      • Talk_18: Applications of generation – Daniel Irvine
      • Talk_19: Framed bordism and Lagrangian embeddings of exotic spheres – Kevin Sackel
      • Problems: Open problems and possible future prospects
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East Coast Pre-Workshop

A pre-workshop on the East Coast will be held on May 12 at Columbia University. Notes, courtesy of Orsola Capovilla-Searle, are now available.

Schedule:

8:30 – 9:00: Breakfast

10:00 – 11:00 Meet & Greet, Break, Discussion
12:00 – 2:00 Lunch
3:00 – 3:30 Break

West Coast Pre-Workshop

A pre-workshop on the West Coast was held on May 5 at Stanford University. Notes, courtesy of Cédric De Groote are available: just click the speaker’s name.

1) [Maxim Jeffs (Berkeley) – Floer theory and symplectic topology]  An introduction to pseudo-holomorphic curves, as well as grading and the signs in Floer theory. This will be important for our workshop. A sample application could be versions of the PSS isomorphism (e.g. HF(L,L) = H(L) for a compact exact Lagrangian). Define symplectic cohomology.
~
2) [Cédric De Groote (Stanford) – Introduction to Fukaya categoriesWe will define the Fukaya category of a symplectic manifold, talk about the wrapping, and introduce various algebraic notions that revolve around it: A_\infty structures, twisted complexes and the generation criterion.
~
3) [Laurent Côté (Stanford) – Overview of the progress on the nearby Lagrangian conjectureA general overview of the nearby Lagrangian conjecture, what’s been done so far, with all the names, and maybe a run down of the special cases. Maybe a very brief sketch of Fukaya-Seidel-Smith here, and possibly a nod to the micro-local sheaf and Lefschetz fibration parts, and sketch the category theoretic part.
~
4) [Ipsita Datta (Stanford) – Spectral sequences An introduction to spectral sequences: how they work, the Serre spectral sequence, and examples of applications such as the one coming from the filtration of a complex. (https://math.berkeley.edu/~hutching/teach/215b-2011/ss.pdf) Include the example of the homology of the loop space of spheres and/or the Hopf fibration over complex projective spaces. (https://en.wikipedia.org/wiki/Serre_spectral_sequence#Example_computations)
~
5) [No talk, but notes by Catherine Cannizzo (Berkeley) – Local Systems] Define local systems both in terms of locally constant sheaves and in terms of representations of the fundamental groupoid of a space; explain the correspondence between both (this is the important bit). Explain what is homology with coefficients in a local system: homology of a cover of the space with an action by deck transformations (chapter 5 of http://www.indiana.edu/~jfdavis/teaching/m623/book.pdf). State Poincaré duality for non-orientable manifolds, i.e. with coefficients in the orientation local system. State how homology pertaining to the locally constant sheaf is the same as the topological description of homology of the space with coefficients in the corresponding local system. If there remains time, explain how one can incorporate local systems into Lagrangian Floer homology (remark 2.11 in https://arxiv.org/pdf/1301.7056.pdf) (or section 3 of Fukaya-Seidel-Smith’s “The symplectic geometry of cotangent bundles from a categorical viewpoint”).

 

Notes from the Kylerec 2017

Find below notes from the Kylerec 2017. Thank you to our note takers Orsola Capovilla Searle and Cédric De Groote.

TALK 1 Roger Casals
Introduction, types of fillings/fillability
01.roger.C
01.Roger.O

TALK 2 Francois-Simon Fauteux-Chapleau
Kirby calculus for Stein manifolds
02.francois-simon.C
03.francois-simon.O

TALK 3 Orsola Capovilla-Searle
Weinstein handles, contact surgery
03.orsola.C

TALK 4 Alvin Jin
Lefschetz fibrations and open books
04.alvin.C
04.alvin.O

TALK 5 Bahar Acu
Mapping class factorizations as Lefschetz fibration fillings
05.bahar.C
05.bahar.O

TALK 6 Roberta Guadagni
J-holomorphic curves, intersection positivity, automatic transversality
07.roberta.C
06.roberta.O

TALK 7 Emily Maw
McDuff rational ruled classification
06.emily.C
07.emily.O

TALK 8 Agustin Moreno
Wendl planar open book filling result
08.agustin.C
08.agustin.O

TALK 9 Umut Varolgunes
High dimensional J-holomorphic curve classifications of fillings
09.umut.C
09.umut.O

TALK 10 Sarah McConnell
Applications of Wendl’s theorem to classifications of fillings
10.sarah.C
10.sarah.O

TALK 11 Kevin Sackel
Intro to Seiberg-Witten invariants
11.kevin.C
11.kevin.O

TALK 12 Jie Min
Symplectic Kodaira dimension 0
12.jie.C
12.jie.O

TALK 13 Tom Gannon
Fillings of unit cotangent bundles
13.tom.C
13.tom.O

TALK 14 Daniel Alvarez-Gavela
Lisca-Matic distinguishing fillings with SW
14.dani.C
14.dani.O

TALK 15 Ziva Kaye
Flexible + loose
15.ziva.C
15.ziva.O

TALK 16 Momchil Konstantinov
SH, SH+, …
16.momchil.C
16.momchil.O

TALK 17 Cedric De Groote
Ustilovsky (application of SFT invariants, exotic contact)
17.cedric.C
17.cedric.O

TALK 18 Scott Zhang
Contact manifolds with flexible fillings and exotic contact structures
18.scott.C
18.scott.O

Discussion Section 1
discussion1.C

Discussion Section 2
discussion2.C

Discussion Section 3
discussion3.C

All of Cedric’s notes:
1.allnotes.C
2.allnotes.C

All of Orsola’s notes:
allnotes.O