Gökova Geometry / Topology Conferences 12 11 10 09 08 07 06 05 04 03 02 01 00 98 96 95 94 93 92


May 25 - May 30 (2009)
Gökova, Turkey

Invited speakers/participants

A. Juhasz       B. Dubrovin       G. Tian
D. Auroux       K. Yasui       L. Katzarkov
M. McLean       F. Catanese       G. Mikhalkin
Weimin Chen       F. Arikan       I. Itenberg
M. Tange       R. Matveyev       A. Petrunin
P. Ghiggini       P. Rossi       A. Degtyarev
B. Ozbagci       T. Etgü       B. Coskunuzer
S. Salur       O. Santillan       B. Efe
Ö. Ceyhan       M. Kalafat       I. Baykur

Scientific Committee : D. Auroux, Y. Eliashberg, G. Mikhalkin, R. Stern, S. Akbulut

Organizing Commitee : T. Önder, T. Dereli, S. Koçak, S. Finashin, M. Korkmaz, Y. Ozan

This conference is sponsored by NSF and TUBITAK.

The participants of 16th Gökova Geometry - Topology Conference

List of Talks
Firat Arikan    Topological invariants of contact structures and planar open books
The algorithm given by Akbulut and Ozbagci constructs an explicit open book decomposition on a contact three-manifold described by a contact surgery on a link in the three-sphere. In this talk, we'll first improve this algorithm by using Giroux's contact cell decomposition process. Our algorithm gives a better upper bound for the recently defined "support genus invariant" of contact structures. If the time permits, we'll also study contact structures on closed three-manifolds which can be supported by an open book having planar pages with three or four boundary components.
Denis Auroux    Landau-Ginzburg models and mirror symmetry relative to an anticanonical divisor
The goal of these talks will be to explain the extension of mirror symmetry to Kahler manifolds with nontrivial first Chern class (non Calabi-Yau case) and the appearance of "Landau-Ginzburg models" in this context. This will be explained on simple examples (in particular CP1), both from the perspective of the Strominger-Yau-Zaslow conjecture and from that of homological mirror symmetry.
Fabrizio Catanese    Moduli spaces of bidouble covers of the quadric. Deformation types, differentiable types, braid monodromy types
Bidouble covers of the quadric, especially the so called abc-surfaces, gave the strongest counterexamples to the def=diff conjecture of Friedman and Morgan.
The final step of a long chain of arguments, ranging from deformation theory to the theory of smoothings of singularities, was done in joint work with Bronek Wajnryb, using an explicit description of the mapping class group factorizations of certain Lefschetz fibrations in order to assert the diffeomorphism of abc-surfaces with the same b and the same (a+c).
A very difficult open question is whether diffeomorphic abc surfaces, endowed with their canonical symplectic structure, are symplectomorphic to each other. Work in progress with Michael Loenne and Bronek Wajnryb shows how to distinguish irreducible components of these moduli spaces via invariants of the braid monodromy factorization of the branch curve, realizing a first step in the direction of a program set up many years ago by Boris Moishezon.
We show in fact that for surfaces in different families we have inequivalent braid monodromy factorizations, whereas their image in the mapping class groups become equivalent.
I will sketch some new ideas to prove non equivalence of factorizations(for the equivalence relation generated by Hurwitz equivalence and simultaneous conjugation).
Our result leaves however open the question of symplectomorphism of the abc surfaces.
Weimin Chen    Finite group actions on 4-manifolds
This will be a survey of some recent progress about symplectic finite group actions on 4-manifolds, group actions on exotic 4-manifolds, etc.
Boris Dubrovin    Integrable Systems (Mini Course)
Paolo Ghiggini    Tight contact structures on the Seifert manifolds -∑ (2,3,6n-1)
I will prove that the Seifert manifold -∑ (2,3,6n-1) admits exactly n(n+1)/2 distinct tight contact structures up to isotopy, which are distinguished by their Ozsváth-Szabó invariant. A remarkable feature of the proof is that, although the manifolds under consideration are homology sphere, Heegaard Floer homology with twisted coefficients plays an essential role in the proof.
Andras I. Juhasz    The decategorification of sutured Floer homology
Sutured manifolds were introduced by David Gabai to study taut foliations on 3-manifolds, and they proved to be powerful tools in 3-dimensional topology. We define a torsion invariant for sutured manifolds which agrees with the Euler characteristic of sutured Floer homology. The torsion is easily computed and shares many properties of the usual Alexander polynomial. We also compare several norms defined on the homology of a sutured manifold. This is joint work with Stefan Friedl and Jacob Rasmussen.
Mustafa Kalafat    Hyperkahler manifolds with circle actions and the Gibbons-Hawking Ansatz
We show that a complete simply-connected hyperkahlerian 4-manifold with an isometric triholomorphic circle action is obtained from the Gibbons-Hawking ansatz with some suitable harmonic function. This is joint work with Justin Sawon.
Ludmil Katzarkov    Generalized HMS and Cycles
After introducing HMS we will discuss some applications to classical problems in algebraic geometry - cycles on surfaces and Fano Calabi Yaus.
Mark McLean    Computability and exotic contact manifolds
For each n>6, we construct (mainly using handle attaching) a list of contact manifolds C1,C2,C3,... diffeomorphic to the sphere of dimension 2n-1 such that there is no algorithm that tells you which of these manifolds are contactomorphic to C1. The idea of the proof is to reduce this problem to the word problem for groups. These contact manifolds also have the property that every supporting contact form has infinitely many simple Reeb orbits.
Rostislav Matveyev    Decomposing mapping classes into product of positive Dehn twists
Grigory Mikhalkin    Tropical geometry
Dmitri Panov    Non-algebraic Calabi-Yau manifolds via hyperbolic geometry
In this talk we will present a construction of simply connected non-algebraic Calabi-Yau manifolds of real dimension 6. Non algebraic Calabi-Yaus have two types - symplectic and complex. It turns out that simply-connected 4-dimensional hyperbolic orbifolds produce symplectic examples while hyperbolic knots in S^3 produce complex examples. In particular there exists an infinte series of complex structures on 2(S^3 x S^3)#(S^2 x S^4) with trivial canonical bundle. This is a joint project with Joel Fine.
Motoo Tange    Spliced homology spheres and lens space surgery
J.Berge defined knots that yielded lens spaces by integral Dehn surgery over S^3. In this talk we will illustrate lens space surgeries over spliced homology spheres by the generalization of Berge's knots.
Gang Tian    Ricci flow and algebraic geometry
In this talk, I will discuss recent progresses on Ricci flow for Kähler metrics and compare to the study of Ricci flow in dimension 3. I will show how it interacts with classification of algebraic manifolds. I will show how Ricci flow is related to symplectic quotients.
Kouichi Yasui    Corks, plugs and exotic 4-manifolds
It is known that every exotic smooth structure on a simply connected closed 4-manifold is determined by a codimention zero compact contractible Stein submanifold and an involution on the boundary. Such a pair is called a cork. In this talk, we give various examples of cork structures of 4-manifolds. We also introduce new objects which we call plugs. As an application of corks and plugs, we construct pairs of homeomorphic but not diffeomorphic compact Stein 4-manifolds. This is a joint work with S. Akbulut.
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Last updated: June 2009
Wed address: GokovaGT.org/2009