course: New methods in orbifold Gromov-Witten theory

speaker: Alessio Corti (Imperial College London)

abstract: I give an introduction to Gromov-Witten theory of Deligne-Mumford stacks and methods of calculation for toric stacks. The course will cover some of my recent work with Coates, Iritani, Li and Tseng. The focus will be on calculations with examples rather than complete proofs. My relationship with stacks is romantic rather than rigorous. The course will have a list of problems for the student which I will soon post on my teaching page at:

http://www.ma.ic.ac.uk/~acorti/teaching.html

Desirable prerequisites: (1) Basic knowledge of toric varieties, e.g. Chapter I of Fulton's "Introduction to toric varieties"; (2) Some familiarity with Gromov-Witten theory of manifolds, e.g. from "Notes on stable maps and quantum cohomology" by Fulton and Pandharipande.

The course will cover some of the following topics:

1. Toric stacks, enhanced Picard group, Mori cone, the secondary fan. 2. GW invariants of stacks, simple examples. 3 GW theory of weak Fano toric stacks, the I-function and the mirror transformation, small quantum cohomology, simplest examples. 4. The B-model: Hori-Vafa, oscillating integrals, semi-infinite variation of Hodge structures, quantum cohomology and birational geometry, Givental's Lagrangian cone. 5. Representable toric morphisms from toric orbi-curves to toric stacks and recursion relations.

timetable:
Mon 16 Jun, 14:00 - 15:00, Aula Dini
Tue 17 Jun, 14:00 - 15:00, Aula Dini
Thu 19 Jun, 14:00 - 15:00, Aula Dini
Fri 20 Jun, 14:00 - 15:00, Aula Dini
Sat 21 Jun, 11:45 - 12:05, Aula Dini
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