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. |