SEVENTH GÖKOVA
GEOMETRY / TOPOLOGY CONFERENCE
May 29 - June 3 (2000)
Gökova, Turkey
| D. Auroux | Y.-G. Oh | J. Bryan | B. Siebert | |||
| A. Stipsicz | P. Ozsvath | R. Gompf | R. Fintushel | |||
| Y. Eliashberg | R. Matveyev | B. Ozbagci | A. Bertram | |||
| D. Freed | P. Feehan | G. Mikhalkin | I. Smith | |||
| R. Donagi | J. Sawon | B.-L. Wang | G. Matic | |||
| A. Petrunin | S. Salur |
Scientific Committee : G.Tian, R.Stern, C. Vafa, R.Kirby, S.Akbulut
Organizing Commitee : T. Onder, T. Dereli, S. Kocak, S. Finashin
This conference is sponsored by International Symposium Program of TUBITAK (Turkish Scientific and Technical Council).
| Aaron Bertram | Counting rational curves and localization |
| Justin Sawon | TQFT and hyperkähler geometry
Rozansky and Witten proposed a 3-dimensional sigma-model whose target space is a hyperkahler manifold. They conjectured that this theory has an associated TQFT, with Hilbert spaces given by certain cohomology groups of the hyperkähler manifold. On the other hand, there is a certain modified TQFT constructed by Murakami and Ohtsuki using the universal quantum invariant. We explain how the Rozansky-Witten TQFT can be obtained from the latter by applying a "hyperkähler weight system" |
| Yong-Geun Oh | Floer theory and geometry of Lagrangian submanifolds |
| Grigory Mikhalkin | Decomposition into pairs of pants in higher dimensions
A useful tool to study Riemann surfaces (complex 1-manifolds) is their decomposition into pairs of pants. Each pair of pants is diffeomorphic to CP1 minus 3 points. In my talk I show that any hypersurface in a toric variety admits a similar decomposition. The higher-dimensional version of a pair of pants is CPn minus (n+2) hyperplanes. The first interesting example is a decomposition of a quintic surface in CP3 (an irreducible 4-manifold) into 125 "pairs of pants". |
| Aaron Bertram | Counting rational curves and localization II |
| Dan Freed | The Verlinde algebra revisited |
| Sema Salur | Special Lagrangian submanifolds |
| Peter Ozsvath | Holomorphic discs and 3-manifold invariants |
| Gordana Matic | Tight contact structures and taut foliations |
| Denis Auroux | Symplectic maps to projective spaces and applications |
| Ron Donagi | G-bundles, hyperkähler manifolds, and stringy Hodge numbers |
| Jim Bryan | Multiple covers, BPS states, and integrality in
Gromov-Witten theory
The Gromov-Witten invariants of Calabi-Yau 3-folds have been conjecturally related to the numbers of certain BPS states in M-theory by the formula of Gopakumar and Vafa. By computing the contributions of multiple covers of a rigid curve in the 3-fold to the Gromov-Witten invariants, we study and verify this conjecture in series of natural cases. This also sheds light on the relationship between the Gromov-Witten invariants and the enumerative geometry of the 3-fold. |
| Bernd Siebert | The symplectic isotopy problem |
| Burak Ozbagci | Commutators, Lefschetz fibrations and the signatures of bundles |
| Andras Stipsicz | Lefschetz fibrations: properties and applications |
| Sergey Finashin | Exotic knottings of surfaces in CP2 |
| Robert Gompf | Topologically characterizing symplectic manifolds |
| Ivan Smith | Lefschetz fibrations and the moduli space of curves |
| Paul Feehan | Non-abelian monopoles and Four-manifold invariants |
| Rostislav Matveyev | Lefschetz fibrations on S1xM3 |
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The participants of 7th Gökova Geometry - Topology Conference (other photos)
Table of contents of the proceedings
- Symplectic maps to projective spaces and sypmlectic invariants
Denis Auroux - Evidence for a conjecture of Pandharipande
Jim Bryan - G-bundles on abelian surfaces
Jim Bryan, Ron Donagi and Conan Leung - Surface bundles: some interesting examples
Jim Bryan, Ron Donagi and Andras Stipsicz - Knotting of algebraic surfaces
Sergey Finashin - The canonical class of a 4-manifold
Ronald Fintushel and Ronald Stern - The Verlinde algebra is twisted equivariant K-theory
Daniel S. Freed - The topology of symplectic manifolds
Robert E. Gompf - On the tautological ring of
Tom Graber and Ravi Vakil - Floer homology and its continuity for non-compact Lagrangian submanifolds
Yong-Geun Oh - Topological quantum field theory and hyperkähler geometry
Justin Sawon - Torus fibrations on symplectic four-manifolds
Ivan Smith - Sections of Lefschetz fibrations and Stein fillings
Andras Stipsicz