Holomorphic Foliations and Symplectic Fillings

General Information:

Place: 1.023 (BMS Seminar room) Johann von Neumann Haus, Rudower Chaussee 25, 12489 Berlin

Time: Mondays 13:15-14:45 (April-July 2026)

Credits: 5 LP for local students

Moodle: If you plan to participate in the seminar, please join the moodle (the enrollment key is "foliation"). The moodle will be used for occasional time-sensitive announcements. Users affiliated with the HU can access moodle using their HU username and password. Non-HU users can access it by following this link and then clicking on "Create new account".

Overview: This is a working group seminar run by Chris Wendl, Thomas Walpuski and Klaus Mohnke. This semester (SoSe 2026), the seminar has a general theme: Holomorphic foliations and symplectic fillings.

The goal is to understand some of the important results in the problem of classifying symplectic fillings of certain nice classes of contact 3-manifolds. This is a very important yet difficult problem in the field of contact and symplectic topology. The main technology we focus on is SFT compactification of pseudoholomorphic foliations on contact manifolds and their fillings, as well as intersection theory.

The topics of the seminar are well-complemented to the SFT (Symplectic Field Theory) course run by Prof. Wendl, as these provide many applications of all the technology developed in that course.

Seminar Plan: A more detailed description of the subject and topics of the talks with corresponding references can be found in this seminar plan.

Prerequisites: It is a bit difficult to write precisely a general set of prerequisites. One definitely needs to be acquainted with basic differential geometry (at least DiffGeo 1 at HU) and some algebraic topology (Topology 1 at HU). Some knowledge of  the main objects in symplectic / contact geometry is definitely very helpful, but I would say one can still pick that up pretty quickly. At this point, I can broadly divide the talks into two kinds: 

1. Technology: This requires some understanding of functional analysis, and willingness to learn some SFT (hopefully you will pick up stuff from the parallel SFT course).

2. Applications: This requires some understanding (or rather, willingness to develop said understanding) of basic low-dimensional geometric topology.

If you would like to participate and / or prepare for a talk, but are not sure about your background, please feel free to write an email to: apratim.choudhury@hu-berlin.de . We can then set up a meeting and discuss further.

Talks: Here is a tentative list of topics to be distributed among the (willing) participants. A more detailed description of each talk can be found here.

• 13.04.26 : General introduction and planning for the semester - Apratim

• 20.04.26 : A crash course on holomorphic curves and Symplectic field theory - Gerard

• 27.04.26 : McDuff's classification of rational and ruled surfaces - Medha

• 04.05.26 : Classification of symplectic fillings of S^3

• 11.05.26 : Classification of symplectic fillings of planar contact 3-manifolds I: Geometric topological objects and main results

• 18.05.26 : Classification of symplectic fillings of planar contact 3-manifolds II: Holomorphic foliations and intersection theory -Kevin

• 25.06.26 : Holiday

• 01.06.26 : Application of Wendl's classification: Fillings of lens spaces - 

• 08.06.26 : A recap of the developed technology and a reminder of the big picture - Apratim / Gerard

• 15.06.26 : Hierarchy of symplectic filling obstructions

• 22.06.26 : Spinal open book decompositions and symplectic fillings I: Geometric topological objects and main results

• 29.06.26 : Spinal open book decompositions and symplectic fillings II: Understanding the technology - 

• 06.07.26 : Symplectic fillings with exotic fibers

• 13.07.26 : A note on contact manifolds with infinite fillings ?? ( AND / OR ) A review of open questions ??

• 20.07.26?? : (Bonus??) Algebraic planar torsion in contact manifolds