Princeton Informal Topology Summer School 2026

Mentors: Fraser Binns, Anubhav Mukherjee, Peter Ozsváth, Zoltán Szabó, Joshua Wang, Luya Wang

General information

For the first six weeks (June 8 - July 17), there are four reading projects:

1. Morse theory and the beginnings of Floer homology
2. Grid homology
3. Knot polynomials and categorification
4. Applications of gauge theory to 4-manifold diffeomorphisms

For the rest of the summer, there will be four research projects, which roughly speaking are extensions of the four reading projects.

Each student is expected to choose two of the four reading projects to complete and to join a single research project.

Each project has a weekly meeting. The weekly meeting consists of:

• A student presentation
• Questions and discussion with a mentor
• Forming a plan for reading and exercises for the following week.

Every student who will be on campus is expected to present at least once throughout the six weeks.

In addition to weekly project-specific meetings, there will be Zoom office hours that are not project-specific.

Morse theory and beginnings of Floer homology

Meetings: Mondays 10am in Fine 1201

Reading:

• Morse Theory by Milnor
• Morse Theory and Floer homology by Audin and Damian

Grid homology

Meetings: Tuesdays 10am in Fine 1201

Webpage

Reading:

• Grid homology for knots and links by Ozsváth, Stipsicz, and Szabó

Knot polynomials and categorification

Meetings: Wednesdays 10am in Fine 1201

Reading:

• "Knots, polynomials, and categorification" by Rasmussen
• "On Khovanov's categorification of the Jones polynomial" by Bar-Natan

Applications of gauge theory to 4-manifold diffeomorphisms

Meetings: Thursdays 10am in Fine 1201

Reading:

• "Diffeomorphism groups and gauge theory for families" by Konno
• "Obstructions to smooth group actions on 4-manifolds from families Seiberg-Witten theory" by Baraglia
• "Constraints on families of smooth 4-manifolds from Bauer-Furuta invariants" by Baraglia
• "Diffeomorphisms of 4-manifolds" by Wall
• "C.T.C. Wall's 1964 articles on 4-manifolds" by Powell