SYZ Mirror Symmetry & Gross-Siebert

We will meet on Thursdays from 2:45PM to 4:15PM at 2-255, for a 1 hour talk followed by a 30 minute discussion session. 

The goal of this reading seminar is to understand some parts of the Gross-Siebert program. We will start with the basics of SYZ mirror symmetry, Lagrangian fibrations and discuss a specific example due to Abouzaid-Sylvan. After the spring break, we will cover some aspects of the Gross-Siebert program, following the references below. The first half will be of a symplectic flavor, while we expect the second half to be closer to algebraic (logarithmic) geometry. 

Please feel free to ask questions to the organizers Yonghwan Kim (yonghkim@mit.edu) and Honghao Jing (honghao@math.harvard.edu).

We also have two mentors (Sam and Sebastian), so reach out for help if you need help preparing the talks.

Schedule

Week 1 (Feb 12) Overview (Yonghwan Kim)

Week 2 (Feb 19) SYZ mirror symmetry and affine structures [Gro08], [Aur07] (Jiarui Wen)

Week 3 (Feb 26) Auroux's focus-focus system [Aur07], [Aur09] (Donghae Lee)

Simons Workshop on Contact Geometry

Week 4 (Mar 12) Local SYZ singularities, following Abouzaid-Sylvan [AS21] (Honghao Jing)

Week 5 (Mar 19) Theta functions and wall structures [GS11] (Sebastian Haney)

MIT Spring Break

Week 6 (Apr 2) Introduction to tropical and log geometry [Ogu18], [Gro11, Ch. 3] (Dylan Toh)

Week 7 (Apr 9) Intrinsic mirror symmetry [GS18] (Samuel Johnston)

Week 8 (Apr 16) Punctured Gromov-Witten invariants 

Week 9 (Apr 23) Punctured Gromov-Witten invariants and theta functions (Ajith U. Kamaran)

Week 10 (Apr 30) Concluding lecture

Suggested references

Abramovich, Chen, Gross, Siebert 25 - Punctured logarithmic maps

Abouzaid 14 - Family Floer cohomology and mirror symmetry

Abouzaid, Sylvan 21 - Homological mirror symmetry for SYZ singularities

Auroux 07 - Mirror symmetry and T-duality in the complement of an anticanonical divisor

Auroux 09 - Special Lagrangian fibrations, wall-crossing, and mirror symmetry

Evans 23 - Lectures on Lagrangian torus fibrations

Gross 08 - The Strominger-Yau-Zaslow conjecture: From torus fibrations to degenerations

Gross 11 - Tropical geometry and mirror symmetry

Gross, Hacking, Siebert 22 - Theta functions on varieties with effective anti-canonical class

Gross, Siebert 11 - From real affine geometry to complex geometry

Gross, Siebert 22 - The canonical wall structure and intrinsic mirror symmetry

Gross, Siebert 18 - Intrinsic mirror symmetry and punctured Gromov-Witten invariants

Gross, Siebert 16 - Theta functions and mirror symmetry

Ogus 18 - Lectures on logarithmic geometry