"Holomorphic two-forms and GW-invariants."
"Combinatorial cobordism maps in hat Heegaard Floer theory."
"Gromov-Witten theory and Noether-Lefschetz theory."
"The Geometry of Genus-One Gromov-Witten Invariants and Mirror Symmetry"
Abstract:
The mirror symmetry principle of string theory has led
to astounding predictions for counts of holomorpic curves.
The verification of the original 1991 prediction for genus-zero
GW-invariants of a quintic threefold (Q3) in the mid 1990s
was quickly followed by proofs of MS formulas for genus-zero
invariants of other manifolds. On ther other hand, the 1993
genus-one BCOV prediction for Q3 (and other positive-genus
MS formulas) remained elusive until recently.
I will describe geometric properties of genus-one invariants
that make them about as computable as genus-zero invariants.
In particular, they lead to the proof of the genus-one BCOV prediction
for Q3, by applying the classical localization theorem and making
use of genus-zero MS formulas.
"PSS-isomorphism revisited''
Abstract :
In this talk, we unravel a critical flaw in the picturesque `proof' by Punikhin-Salamon-Schwarz of the commonly called PSS-isomorphism between the quantum cohomology and the Floer cohomolgy. Then we explain a new gluing analysis to complete construction of the PSS-cobordsim entering in the suggested proof. This was originally indicated just by the picture without details. This is a joint work with Ke Zhu.
"Functoriality of Gromov--Witten theory under K-equivalent transformations"
Abstract:
I will discuss how GW invariants behave under K-equivalent birational transformations. This is a joint program with H.-W. Lin and C.-L. Wang.
"Analytic open string amplitude for toric Calabi-Yau form matrix model"