Math 290 - Seminar on Mirror Symmetry

Math 290 - Seminar on Mirror Symmetry - Spring 2016

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

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:

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

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)

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)