The goal of these lectures is to study the algebraic construction of categorical enumerative invariants from a cyclic A-infinity category and a splitting of the Hodge filtration due to Caldararu—Costello—Tu, and its relation to topological conformal and Deligne—Mumford field theories.

The precise content of the course can be amended at the beginning of the semester based on the common interests of the students.

You can find here the course plan and a poster.

Planning

Room : seminar room of QM

• February, Room TBD, blabla, Notes TBW.

References

• Kevin J. Costello, Topological conformal field theories and Calabi—Yau categories, 2007

• Andrei Caldararu, Kevin J. Costello, Junwu Tu, Categorical Enumerative Invariants, I: String vertices, 2020

• Andrei Caldararu, Junwu Tu, Effective Categorical Enumerative Invariants, 2024

• Amanda Hirschi, Kai Hugtenburg, An open-closed Deligne—Mumford field theory associated to a Lagrangian submanifold, 2025

 

Last update November 15, 2025.