# GT seminar: "Relative Wrapped Fukaya Categories of Surfaces"

- Date: 10 October 2024, 13:15–14:15
- Type: Seminar
- Lecturer: Daniil Mamaev (UCL)
- Organiser: Matematiska Institutionen
- Contact person: Alex Takeda

Daniil Mamaev (Imperial College London) will give a seminar talk.

**Abstract **Relative wrapped Fukaya categories of surfaces arise naturally in homological mirror symmetry in two ways. As mirrors to some relative curves and, conjectured by Lekili-Segal, as mirrors to the total spaces of algebraic torus fibrations over bordered surfaces. After giving motivating examples I will sketch an explicit construction of a triangulated relative wrapped Fukaya category of a surface directly from geometric data, without the use of triangulated envelopes or A-infinity quotients. Then I will explain why the curves with isotopic Legendrian lifts to the contactisation give quasi-isomorphic objects in the category and state a generation criterion that in particular implies that in the non-relative case the newly constructed category is equivalent to the topological Fukaya category of Haiden-Katzarkov-Kontsevich.

The talk is based on a work in progress towards a PhD under the supervision of Yanki Lekili.

This is a talk in our geometry and topology seminar series.