Mathematics

Topics:

1. A review of Fulton-MacPherson intersection theory.
2. Cones, normal cones, lci morphisms and reduced cotangent complex.
3. Groupoids, 2-categories and stacks.
4. Deligne-Mumford and Artin algebraic stacks.
5. Abelian cone stacks and derived category; normal cone stack.
6. Perfect obstruction theories and virtual classes.
7. Functorial properties of virtual classes and pullbacks.
8. Gromov-Witten invariants: definition and proof of the
Kontsevich-Manin axioms.

If there is interest, more talks could be organized later in the year
on more advanced topics (e.g., virtual localization, degeneration
formulas, Donadson and Donaldson-Thomas invariants).