D. Auroux - Tuesdays, 2-3:30pm, Room 939 Evans

This seminar will revisit the themes of past seminars (see here, here, here and here) on geometric aspects of mirror symmetry.

The details are to be determined based on the participants' interests. Possible topics for this semester are as follows:

- Lagrangian Floer homology and Fukaya categories
- Lagrangian fibrations, family Floer homology and HMS, after Abouzaid
- Liouville sectors and their Fukaya categories, after Ganatra-Pardon-Shende

We will also hear from some of the participants about their own work or related topics.

Prerequisite: some knowledge of symplectic geometry, ideally including prior exposure to J-holomorphic curves.

**Tuesday 8/29**: First meeting and overview (D. Auroux)**Tuesday 9/5**: Lagrangian Floer homology (D. Tonkonog)**Tuesday 9/12**: Lagrangian Floer homology continued (D. Tonkonog)**Tuesday 9/19**: Families of Lagrangian tori with local systems and analytic dependence (D. Auroux) (Notes)**Tuesday 9/26**: Family Floer theory (D. Auroux + J. Hicks)**Tuesday 10/3**: Family Floer theory continued? (J. Hicks?)**Tuesday 10/10**: Umut Varolgunes (MIT)**Tuesday 10/17**: HMS for toric varieties (Abouzaid's thesis) (M. Jeffs)?**Tuesday 10/24**: More on admissibility, mirrors of toric varieties, etc. (A. Hanlon)?

Notes from past seminars and courses on the topic:

- Fall 2009 topics course on mirror symmetry (Oct 15-Dec 1 lectures)
- Fall 2011 seminar (see also the Spring 2011 seminar)
- Fall 2016 Eilenberg lectures on Fukaya categories and HMS

- P. Seidel,
*Fukaya categories and Picard-Lefschetz theory*, Zurich Lectures in Advanced Mathematics, European Math. Soc., Zurich, 2008. - D. Auroux,
*A beginner's introduction to Fukaya categories*, Contact and Symplectic Topology, Bolyai Soc. Math. Stud.**26**, Springer, 2014, pp. 85-136. (arXiv:1301.7056)

- M. Abouzaid,
*Family Floer cohomology and mirror symmetry*, Proceedings of 2014 ICM (arXiv:1404.2659) - M. Abouzaid,
*The family Floer functor is faithful*, (arXiv:1408.6794) - M. Abouzaid,
*Homological mirror symmetry without corrections*, (arXiv:1703.07898)

- M. Abouzaid,
*A geometric criterion for generating the Fukaya category*, Publ. Math. IHES**112**(2010), 191-240 (arXiv:1001.4593) - S. Ganatra, J. Pardon, V. Shende,
*Covariantly functorial Floer theory on Liouville sectors*, (arXiv:1706.03152)