
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 threemanifold described by a contact surgery on a link in the threesphere. 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 threemanifolds which can be supported by an open book having planar pages with three or four boundary components.


Denis Auroux  
LandauGinzburg 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
CalabiYau case) and the appearance of "LandauGinzburg models" in
this context. This will be explained on simple examples (in particular
CP^{1}), both from the perspective of the StromingerYauZaslow 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 abcsurfaces,
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 abcsurfaces 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 4manifolds
This will be a survey of some recent progress about symplectic finite group actions on 4manifolds, group actions on exotic 4manifolds, etc.


Boris Dubrovin  
Integrable Systems (Mini Course)


Paolo Ghiggini  
Tight contact structures on the Seifert manifolds ∑ (2,3,6n1)
I will prove that the Seifert manifold ∑ (2,3,6n1) admits exactly
n(n+1)/2 distinct tight contact structures up to isotopy, which are distinguished by their
OzsváthSzabó 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
3manifolds, and they proved to be powerful tools in 3dimensional 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 GibbonsHawking Ansatz
We show that a complete simplyconnected
hyperkahlerian 4manifold with an isometric triholomorphic circle
action is obtained from the GibbonsHawking 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 2n1
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  
Nonalgebraic CalabiYau manifolds via hyperbolic geometry
In this talk we will present a construction of simply connected nonalgebraic CalabiYau manifolds of real dimension 6. Non algebraic CalabiYaus have two types  symplectic and complex. It turns out that simplyconnected 4dimensional 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 4manifolds
It is known that every exotic smooth structure on a simply connected
closed 4manifold 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
4manifolds. 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 4manifolds. This is a joint work with S. Akbulut.

