# Conferences and lectures

## Kavli IPMU-FMSP Tutorial Workshop "Geometry and Mathematical Physics"

2013-01-22 ~ 01-25

Lecture Hall, Kavli IPMU

List of lecturers:

Alexey Bondal

Kentaro Hori

Todor Milanov

Yukinobu Toda

### Tentative Schedule

Tuesday, Jan. 22

10:30 - 12:00 Milanov I

13:30 - 15:00 Milanov II

15:30 - 17:00 Toda I

Wednesday, Jan. 23

10:30 - 12:00 Milanov III

13:30 - 15:00 Toda II

15:30 - MS Seminar

Thursday, Jan. 24

10:30 - 12:00 Hori I

13:30 - 15:00 Toda III

15:30 - MS Seminar

Friday, Jan. 25

10:30 - 12:00 Hori II

13:30 - 15:00 Bondal I

15:30 - 17:00 Bondal II

Information : Toshitake Kohno

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### Todor Milanov (Kavli IPMU)

Title: "The local Eynard--Orantin recursion in Gromov--Witten theory."

Abstract: The Eynard--Orantin topological recursion was first discovered in the settings of matrix models, but its applications are becoming more and more powerful in much more general settings. Given a manifold with semi-simple quantum cohomology, one can construct a certain set of correlation functions that satisfy the Eynard--Orantin recursion. In particular, since the Laurent series expansions of the correlation functions determine the complete set of Gromov--Witten invariants, the recursion allows us to determine all invariants from some very basic (2-point, genus-0) ones. Moreover, it seems that there is a certain twisted vertex algebra representation that governs the entire Gromov--Witten theory. I am planning to give an introduction to all these topics. The approximate plan is the following:

Lecture I: Quantum cohomology, Frobenius manifolds, and Givental's higher genus reconstruction formalism.

Lecture II: Primitive forms, period integrals, and Frobenius manifolds.

Lecture III: W-constraints and the Eynard--Orantin recursion.

### Yukinobu Toda (Kavli IPMU)

Title: "Stability conditions and Donaldson-Thomas invariants on Calabi-Yau 3-folds."

Abstract: I will give an introduction to Donaldson-Thomas (DT) invariants on Calabi-Yau 3-folds, which are virtual counting of semistable sheaves on them. Then I explain how stability conditions on derived categories of coherent sheaves are useful for the study of DT invariants. If time permits, I will also list some open problems, and discuss some new results on them.