Berkeley Student Floer Seminar: Symplectic Field Theory, Fall 2025

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Time & Location: Fridays 11am–12pm, Evans 939 (I have the room until 12:30pm for extra discussions).

Symplectic Field Theory (SFT) is a package of invariants introduced by [EGH] and associated to symplectic and contact manifolds. SFT is based around counting punctured holomorphic curves in non-compact symplectic manifolds. While in various states of well-definedness, these invariants have had many applications to symplectic topology and dynamics and SFT is a guiding philosophy for much contemporary work in symplectic geometry.

Topics

We will very roughly be following Chris Wendl's Lectures on Symplectic Field Theory. An ambitious list of topics we hope to discuss are as follows.

Basics: symplectic cobordisms, stable Hamiltonian structures; pseudoholomorphic curve theory; Hofer energy.
Analysis: SFT compactness; asymptotic markers, coherent orientations, gluing, and good/bad orbits; transversality issues.
Algebraic Invariants: SFT, RSFT, contact homology, and their algebraic structure; cylindrical contact homology, augmentations, and LCH; alternative formulations.
Constructions: CCH via Bao–Honda and Hutchings–Nelson, LCH as equivariant SH via Bourgeois–Oancea, and CH via Pardon; comparison with ECH via Hutchings; polyfolds.
Computations: algebraic overtwistedness; Morse–Bott methods; string topology; examples of CH.
Applications: GW invariants; classifying contact structures; algebraic torsion and embedding complexity; symplectic capacities; contact dynamics.

Schedule

Date	Speaker	Title	References/Notes
29 August	Gabriel Beiner	Logistics and Introduction to SFT	[Wen, chapter 1], [HS], notes
5 September	Nancy Mae Eagles	Preliminaries and Hofer Energy	[Wen], [Hof], notes
12 September	Ward Veltman	Hessians and Cauchy–Riemann type operators in SFT	[Wen, chapters 3–5], notes
19 September	Ward Veltman	Hessians and Cauchy–Riemann type operators in SFT cont.	[Wen, chapters 3–5], notes
26 September	Robert Bowden	Initial Transversality Results in SFT	[Wen, chapters 6–7]
3 October	Gabriel Beiner	Generic Transversality in SFT	[Wen, chapters 8, 12], notes
10 October	Galen Liang	SFT Compactness	[Wen, chapter 9], notes
17 October	Galen Liang	SFT Compactness cont.	[Wen, chapter 9], notes
24 October	Joseph Hlavinka	Coherent Orientations and Gluing	[Wen, chapter 11]
31 October	Joseph Hlavinka	Coherent Orientations cont.	[Wen, chapter 11], [BM]
7 November	Ward Veltman	The Generating Function of SFT	[Wen, chapter 12]
14 November	Gabriel Beiner	Extracting Invariants from SFT	[Wen, chapter 13], [EGH], notes
21 November	Galen Liang	Contact Homology and Morse–Bott Methods	[Bou], notes
5 December	Katrin Wehrheim	Regularization of Moduli Spaces from Geometric Methods to Polyfold Theory	[FFGW]
12 December	Gabriel Beiner	Some Applications of SFT	[LW], [Sie], [CT]

References

Here are some helpful references for the seminar (more to be added as we progress).

[EGH] Eliashberg, Givental, Hofer, Introduction to Symplectic Field Theory.
[Wen] Wendl, Lectures on Symplectic Field Theory.
[HS] Hind, Siegel, Symplectic field theory: an overview.
[BEHWZ] Bourgeois, Eliashberg, Hofer, Wysocki, Zehnder, Compactness results in SFT.
[BM] Bourgeios, Mohnke Coherent orientations in SFT.
[Hof] Hofer. Curves in symplectizations and the Weinstein conjecture.
[FFGW] Fabert, Fish, Golovko, Wehrheim, Polyfolds: A first and second look.
[Par] Pardon, Contact homology and VFCs.
[HN] Hutchings, Nelson, S^1-equivariant contact homology for hypertight contact forms.
[BH] Bao, Honda, Definition of CCH in dimension three.
[Bou] Bourgeois, A Morse–Bott approach to contact homology.
[LW] Latschev, Wendl, Hutchings, Algebraic torsion in contact manifolds.
[Sie] Siegel, Higher symplectic capacities.
[CT] Chaidez, Tanny Elementary SFT spectral gaps and the strong closing property.