CY Manifolds and Mirror symmetry

We will meet on Thursdays from 3:00PM to 4:30PM at 2-255, for a 1 hour talk followed by a 30 minute discussion session. 

The goal of this reading seminar is to understand the statement of Hodge-theoretic mirror symmetry relating Gromov-Witten invariants from the A-side, and period integrals from the B-side for Calabi-Yau manifolds. This seminar is intended as a baby version of the KKPY seminar. We will mostly follow the books [CK] and [GHJ], and a rough outline of the talks can be found here.

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

Schedule

Week 1 (Sep 25) Overview - the quintic 3-fold (Yonghwan Kim) Notes

Week 2 (Oct 2) Hodge theory (Guangxi Yan) Notes

Week 3 (Oct 9) Hodge theory meets birational geometry (Andrew Burke) Notes

Week 4 (Oct 16) Introduction to symplectic Gromov-Witten invariants (Kenny Blakey) Notes

Week 5 (Oct 23) Gromov-Witten invariants from algebraic geometry (Anne Larsen)

Week 6 (Oct 30) Computing Gromov-Witten invariants: equivariant localization (Jiarui Wen)

Week 7 (Nov 6) Quantum cohomology (Honghao Jing)

Week 8 (Nov 13) TBD - depends on the audience

Week 9 (Nov 20) Quantum differential equations (Yonghwan Kim)

Thanksgiving week

Week 10 (Dec 4) Givental's I-function and wrap-up (Sebastian Haney)

Suggested references

Auroux, Lecture notes on mirror symmetry link

Batistella, Carocci, Manolache, Virtual classes for the working mathematician

Behrend, Gromov-Witten invariants in algebraic geometry

Clemens, Griffiths, The intermediate Jacobian of the cubic threefold

Cox, Katz, Mirror symmetry and algebraic geometry

Fulton, Pandharipande, Notes on stable maps and quantum cohomology

Gross, Huybrechts, Joyce, Calabi-Yau manifolds and related geometries

Graber, Pandharipande, Localization of virtual classes

Kock, Vainsencher, An invitation to quantum cohomology

Kontsevich, Katzarkov, Pantev, Hodge theoretic aspects of mirror symmetry

Voisin, Hodge theory and complex algebraic geometry