| 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
| 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.