Seminar on Gromov-Witten Theory

Winter 2012
Math 290, CRN 40271
Tuesday 10am-noon
2240 MSB

January 10. Olivia Dumitrescu: The number of rational curves on the projective plane, after Kontsevich, part I.

The EO formula is speculated to be also applicable to non-Calabi-Yau cases such as projective spaces. This talk will explore the possibility for the projective plane. In the first talk Olivia will explain the beautiful work of Kontsevich on counting rational curves.

January 17. Olivia Dumitrescu: The number of rational curves on the projective plane, after Kontsevich, part II.

January 24. Adam Sorkin: An introduction to stability conditions, part I.

Stability conditions are introduced via semistable vector bundles on curves, in the sense of Mumford. A close look at the properties such vector bundles posses will be abstracted to abelian/triangulated categories.

January 31. Motohico Mulase: A new recusion for Grothendieck's dessins d'enfants.

February 7. Adam Sorkin: An introdution to stability conditions, part II.

In the second part, the space of stability conditions will be examined. Particular attention will be paid to group actions on said space.

February 14. Adam Sorkin: An introduction to stability conditions, part III.

In the final(?) lecture on this topic, we will examine the local topology on the space of stability conditions, and review the state of knowledge on stability manifolds.

February 28. Motohico Mulase: Quantum Catalan Numbers.

March 6. Adam Sorkin: The Cherednik algebra of an Algebraic Curve.

March 13. Olivia Dumitrescu: The closed topological vertex via Cremona Transform.

Computing the GW invariants of the 'closed vertex' in terms of ordinary GW invariants of blow ups of P^3's.