Kobe Workshop on Quantum Cohomology and Mirror Symmetry
Abstract
Rahul Pandharipande (Princeton University)
Modern enumerative geometry I and II
I. I will discuss three approaches to enumerative geometry for 3-folds: GW theory, DT theory, and the more recent theory of stable pairs in the derived category. All are conjectured to be equal.

II. I will discuss aspects of the theory of stable pairs in the derived category: toric geometry, K3 geometry, and descendent calculations. Joint work with R. Thomas.

Mark Gross (University of California, San Diego)
Mirror symmetry and affine manifolds
I will survey my recent joint work with Siebert.

Shinobu Hosono (University of Tokyo)
Fourier-Mukai partners and Gromov-Witten invariants
I will talk about mirror symmetry of Fourier-Mukai partners of a K3 surface of degree 12, and its three dimensional analogue. In particular, I will show predictions for Gromov-Witten invariants (g>0) of Calabi-Yau threefolds which are derived equivalent but not birational. [Based on collaborations with B. Lian, K. Oguiso and S.-T.Yau (2002--2004) and a recent calculation with Y. Konishi (hep-AG/0704.2928)]

Hiroshi Iritani (Kyushu University)
On the Kaehler moduli space of P^1
I will introduce a real structure in quantum cohomology which yields a Hermitian metric (tt* geometry) on the Kaehler moduli space. I will explain the easiest case of P^1 whose tt* geometry was calculated by Cecotti-Vafa more than ten years ago.

Kota Yoshioka (Kobe University)
Moduli of coherent sheaves on a blown-up surface
I will compare the moduli space of coherent sheaves on a surface $X$ with that on a blow-up $\widehat{X}$ by using the moduli of coherent sheaves with torsions.
This is a joint work with Hiraku Nakajima.