##
Math 290 - Seminar on Mirror Symmetry - Spring 2016

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

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Outline

This seminar will continue last Fall's seminar
(see here), in slightly different directions,
focusing on more geometric aspects of mirror symmetry.

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

- Lagrangian torus fibrations and the SYZ conjecture
- Lagrangian tori in conic bundles and SYZ mirror symmetry for hypersurfaces
- Family Floer homology and family Floer functor

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

###
What's happening

- NO MEETINGS ON Tuesdays 1/19 and 1/26
**Tuesday 2/2**: first meeting (D. Auroux) -- introduction to SYZ
**Tuesday 2/9**: geometry of Lagrangian torus fibrations (D. Auroux)
**Tuesday 2/16**: enumerative geometry and superpotentials (D. Auroux)
**Tuesday 2/23**: instanton corrections: an example (D. Auroux)
**Tuesday 3/1**: SYZ for hypersurfaces in toric varieties (C. Cannizzo)
(Notes)
**Tuesday 3/8**: NO SEMINAR
**Tuesday 3/15**: family Floer homology (B. Gammage)
(Notes)
**Tuesdays 3/22, 3/29**: NO SEMINAR
**Tuesday 4/5**: microlocal sheaves (B. Gammage)
**Tuesday 4/12**: microlocal sheaves on pairs of pants
(B. Gammage / Yingdi Qin)

###
Possible References

Notes from past seminars and courses on the topic:

Possible references:
- 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)
- A. Polishchuk, E. Zaslow,
*Categorical mirror symmetry: the elliptic
curve*, Adv. Theor. Math. Phys. 2 (1998), 443-470;
arXiv:math.AG/9801119
- D. Auroux,
*Mirror symmetry and T-duality in the complement of an
anticanonical divisor*,
J. Gökova Geom. Topol. 1 (2007), 51-91;
arXiv:math/0706.3207
- M. Abouzaid, D. Auroux, L. Katzarkov,
*Lagrangian fibrations on
blowups of toric varieties and mirror symmetry for hypersurfaces*,
arXiv:math/1205.0053
- M. Abouzaid,
*Family Floer cohomology and mirror symmetry*,
Proceedings of 2014 ICM,
(arXiv:1404.2659)