Introduction to Gromov-Witten invariants, II

Abstract: The goal of this crash course is to introduce the basic notions of moduli space of stable maps and Gromov-Witten invariants. In particular when the stable maps have rational domain and the target is a projective space.

Description: The course is split in 5 main parts. We will cover the following topics, time permitting.
(1) Basic definitions.
(2) The case of genus 0: boundary divisors and examples.
(3) Gromov-Witten invariants.
(4) Quantum cohomology.
(5) Kontsevich-Atiyah-Bott formula.

If time permits, we will give some enumerative applications.

Main References:

[CK99] D. A. Cox and S. Katz, Mirror symmetry and algebraic geometry, AMS, 1999.
[FP97] W. Fulton and R. Pandharipande, Notes on stable maps and quantum cohomology, Algebraic geometry—Santa Cruz 1995, Proc. Sympos. Pure Math., 62, AMS, 1997.
[HTK+03] K. Hori, R. Thomas, S. Katz, C. Vafa, R. Pandharipande, A. Klemm, R. Vakil, and E. Zaslow, Mirror symmetry, vol. 1, AMS, 2003.

mathematical physicsalgebraic geometryalgebraic topologydifferential geometryrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry and Physics @ Lisbon