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Events
Mirror symmetry and tropical geometry reading group

MPI für Mathematik in den Naturwissenschaften Leipzig

G3 10 (Lecture hall)

conference

17/05/2023 17/05/2023

Mirror symmetry and tropical geometry reading group

This reading group aims at exploring the links between tropical geometry and mirror symmetry. We will follow quite closely (up to some action of the symmetric group of some subsets of the (sub)sections) the book [5]. The ultimate goal is to go through the first three chapters of the book. The format would be the following: each talk would be between one hour and one hour and a half long, we will meet every two weeks (alternating between Chemnitz and Leipzig) for two or three talks in a row - this depends mostly on the audience and the (hopefully non-empty!) intersection of our availabilities. It would be nice (if you have time!) if everyone could write down their talk in TeX in such a way we can put everything together afterwards.

Program

10:00 - 11:15	Maximilian Wiesmann (Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany) Stable pointed curves and stable maps In that talk, follow the section 2.1. of [5]. As in the book, take stacks as a black box (maybe you can give a rough idea about it: we like quotients to exists but the non-triviality of the stabilizer(s) is usually a problem for the quotient to exist as a scheme, hence we have to pass to stacks; in our case, the groups in questions are group of automorphisms2, passing to stacks will make more functors representable. Since things could seem a little hidden under the carpet here, put the emphasis on the examples and especially on the Gromov-Witten invariant since it will be important in the sequel: this is the object for curves counting and it comes into the play in the definition of quantum cohomology. Explain the manifestation of stacky phenomena in Gromov-Witten invariants (when they are not a natural number).
11:30 - 12:45	Luca Giovenzana (TU Chemnitz) Quantum cohomology and quantum differential equation In that talk, follow the sections 2.1.2. and 2.1.4. of [5]. Introduce the (big) quantum cohomology on a variety with no odd cohomology and the WDVV equation. Compute the quantum product for P 2. Introduce the quantum differential equation and derive a fundamental set of solutions. The map S(Ti) = si as defined in 2.1.4 will play an important role in the sequel so should be discussed.
13:00 - 14:00	Lunch Break
14:00 - 15:15	Christian Sevenheck (TU Chemnitz) Semi-infinite variations of Hodge structures and moving subspace realisation In that talk, follow the sections 2.1.5. and 2.1.6. of [5]. Define semi-infinite variations of Hodge structure and show how one arises from the quantum cohomology ring. Talk about the moving subspace realisation, again with emphasis on the quantum cohomology example.
15:30 - 16:45	Christian Sevenheck (TU Chemnitz) Frobenius manifolds and semi-infinite variations of Hodge structures

Mirror symmetry and tropical geometry reading group

Program

Scientific Organizers

Maximilian Wiesmann

Administrative Contact

Mirke Olschewski