D. Auroux - Tuesdays, 3:30-5pm, Room 891 Evans

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

**The seminar will continue into Spring 2016 -- still planning for
Tuesdays 3:30-5 in 891 Evans.**

The details are to be determined based on the participants' interests. A possible plan for this semester is as follows:

- Lagrangian Floer homology
- Fukaya categories (ordinary and wrapped)
- Deformation theory, generation criteria, etc.
- Homological mirror symmetry
- Computations: pair of pants, genus 2 curve, etc.
- (time permitting): family Floer homology and family Floer functor

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

Course control number: 54554.

**Tuesday 9/1**: Overview (D. Auroux)**Tuesday 9/8**: Lagrangian Floer cohomology (A. Hanlon)**Tuesday 9/15**: Lagrangian Floer cohomology continued (A. Hanlon)**Tuesday 9/22**: PSS isomorphisms in Lagrangian Floer homology (B. Filippenko)**Tuesday 9/29**: Products in Lagrangian Floer theory, Fukaya category (M. Weiler)**Tuesday 10/6**: Twisted complexes, mapping cones, and generators (D. Auroux)**Tuesday 10/13**: Lagrangian surgery and mapping cones (K.-Y. Fang)**Tuesday 10/20**: Hochschild cohomology and classification of A_infty-structures (J. Hicks)**Tuesday 10/27**: The Fukaya category of the genus 2 curve (C. Cannizzo) (Notes)- Tuesday 11/3: no meeting
**Tuesday 11/10**: The mirror of the genus 2 curve (C. Cannizzo) (Notes)**Tuesday 11/17**: The wrapped Fukaya category (B. Gammage)**Tuesday 11/24**: The wrapped category of the pair of pants and HMS (D. Auroux) (Notes)**Tuesday 12/1**: Open-closed maps and Abouzaid's generation criterion (J. Hicks)- Tuesday 12/8: no meeting

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)

- 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,
*A geometric criterion for generating the Fukaya category*, Publ. Math. IHES**112**(2010), 191-240 (arXiv:1001.4593) - M. Abouzaid,
*A cotangent fiber generates the Fukaya category*, Adv. Math.**228**(2011), 894-939 (arXiv:1003.4449) - M. Abouzaid, D. Auroux, A. Efimov, L. Katzarkov, D. Orlov,
*Homological mirror symmetry for punctured spheres.*, J. Amer. Math. Soc.**26**(2013), 1051-1083 (arXiv:1103.4322) - P. Seidel,
*Fukaya categories and deformations*, Proceedings of 2002 ICM (arXiv:0206155) - P. Seidel,
*Homological mirror symmetry for the genus two curve*, J. Algebraic Geom.**20**(2011), 727-769 (arXiv:0812.1171) - R. Thomas,
*Derived categories for the working mathematician*, Proc. Winter School on Mirror Symmetry (Harvard, 1999), International Press, 2001 (arXiv:0001045) - M. Abouzaid,
*Family Floer cohomology and mirror symmetry*, Proceedings of 2014 ICM (arXiv:1404.2659)