
Peng Lu  
An introduction to reduced distance and reduced volume (Mini course)
Reduced distance and reduced volume are introduced
by Perelman in his 2002 paper "The entropy formula for the Ricci flow
and its geometric applications". Note that the distance function on
a manifold is defined using a Riemannian metric, the reduced distance
on a manifold is defined using a solution to backward Ricci flow.
The reduced distance shares some of the properties of the distance function,
and it also has some beautiful properties of its own. These properties has
fundamental application to Ricci flow. In this minicourse we will
give an introduction to the reduced distance and its application. 

Lenny Ng  
Knot homologies and transverse knots
I'll survey recent progress in the application of knot homologies
(especially knot Floer homology) to the problem of distinguishing
transverse knots in standard contact threespace. 

Anar Akhmedov  
Stein fillings of contact manifolds
We give an infinite family of examples of contact threemanifolds that
each admit infinitely many simply connected, homeomorphic but not
diffemorphic Stein fillings. 

Tolga Etgü  
Partial open book decompositions and relative Giroux correspondence
(joint work with Burak Ozbagci)
I will describe abstract partial open book decompositions of compact 3manifolds with boundary. I will then explain how to associate a sutured manifold to a given partial open book decomposition and construct a compatible (in the sense of Honda, Kazez and Matic) contact structure on this manifold whose dividing set on the convex boundary agrees with the suture. The aim of the talk will be the proof of a relative version of Giroux correspondence, i.e., a onetoone correspondence between isomorphism classes of partial open book decompositions modulo positive stabilization and isomorphism classes of compact contact 3manifolds with convex boundary. 

Çagri Karakurt  
Every 4Manifold is BLF
I will outline the proof that every compact smooth 4manifold X has a
structure of a Broken Lefschetz Fibration (BLF in short). Furthermore, if
b_{2}^{+}(X)>0 then it also has a Broken Lefschetz Pencil structure (BLP)
with nonempty base locus. This improves a previous Theorem of Auroux,
Donaldson and Katzarkov, and our proof is topological, i.e. uses only
4dimensional handlebody theory (this is a joint work with S. Akbulut). 

Yanki Lekili  
Wrinkled fibrations on nearsymplectic manifolds
Motivated by the programmes initiated by Taubes and Perutz, we study the geometry of nearsymplectic 4manifolds and broken Lefschetz fibrations on them. We present a set of four moves which allow us to pass from any given fibration to any other broken fibration which is deformation equivalent to it. The arguments rely on the introduction of a more general class of maps, which we call wrinkled fibrations and which allow us to rely on classical singularity theory. As an application, we disprove a conjecture of Gay and Kirby about essentialness of achiral singularities for broken fibrations on arbitrary closed 4manifolds. 

Özgür Kisisel  
Cotton flow
In this talk, I wish to describe our recent work
(arXiv:0803.1603) with Ö. Sarioglu and B. Tekin concerning a
geometric flow on 3manifolds. Specifically, using the conformally
invariant Cotton tensor on a 3manifold, we define the "Cotton
flow", which tends to evolve initial metrics into conformally flat
metrics. The behaviour of the flow is in sharp contrast with the
Yamabe flow, which preserves conformal classes. The Cotton flow can be
written as the gradient flow of an entropy functional, which coincides
with the gravitational ChernSimons action. I will discuss in detail
the evolution of homogenous geometries under the Cotton flow, and in
particular prove that every homogenous metric on the 3sphere evolves
exponentially to the round sphere metric. A possibly interesting fact
for the formation of singularities is that two of the homogenous
geometries degenerated by the Ricci flow are fixed by the Cotton flow,
whereas the fate of the remaining geometries with respect to the
latter are not worse. 

Robert Lipshitz  
A toy model for knot Floer homology of tangles
We will discuss what happens to the knot Floer invariant
when one cuts a planar grid diagram for a knot in half. This toy
model illustrates most of the structures  and difficulties  which
arise when extending knot Floer homology to tangles. This is joint
work with P. Ozsvath and D. Thurston. 

Paolo Rossi  
Gromov Witten invariants of P1orbifolds and reflection groups of type ADE
Symplectic Field Theory in the target orbifold situation allows us to compute the GromovWitten potential of orbicurves in terms of multiple Hurwitz numbers (counting branched coverings with given ramification profile over the orbifold points). This potential is in general a power series in the cohomology variables. Restricting to the (target) genus 0 case, we address the problem of classifying the P1orbifolds for which this series truncates to a polynomial. Remarkably this classification corresponds, via isomorphisms of the relevant Frobenius manifolds, to the one of (extended affine) Weyl groups of type A,D,E. 

YumTong Siu  
Techniques and problems in application of dbar estimates
to algebraic geometry
I will explain the key arguments in the application of dbar
estimates to algebraic geometric problems, such as the Fujita conjecture,
invariance of plurigenera, and the analytic proof of the finite generation
of the canonical ring. Will discuss open problems, together with possible
approaches, such as the Kaehler case of the invariance of plurigenera and
the abundance conjecture. Will also discuss the other direction which
applies algebraic geometric techniques to regularity problems of partial
differential equations by using the method of multiplier ideal sheaves.


Erwan Brugalle  
Tropical computation of Zeuthen numbers
This is a joint work in progress with B. Bertrand and G.
Mikhalkin. We use the so called "floor decomposition" technic to
compute Zeuthen numbers of projective plane. In the genus 0 case, we
obtain combinatorial formulas involving Hurwitz numbers.


Nermin Salepci  
Classification of real elliptic Lefschetz fibrations via necklace
diagrams
We consider elliptic Lefschetz fibrations over S^{2} together with a
real structure and study the real locus (which is a fibration over
S^{1}) of them.
We show that real locus determines real elliptic Lefschetz
fibrations in case when all critical values are real. We obtain a
decoration on S^{1}
which leads to a combinatorial object which we call necklace
diagrams. Using necklace diagrams we obtain a classification of
real elliptic Lefschetz
fibrations over S^{2} with only real critical values. This
classification gives the real analogue of the wellknown
classification of elliptic Lefschetz fibrations
due to Moishezon and Livné. An explicit list is given for fibrations
with 12 or 24 real critical values.
Necklace diagrams also let us observe some interesting phenomena for
real elliptic Lefschetz fibrations.


Ian Hambleton  
Aspherical 2complexes and 4manifolds
There is a rich class of finitely presented groups which occur as
fundamental groups of aspherical 2complexes. Examples include 1relator groups
(e.g. BaumslagSolitar groups), small cancellation
groups, and random groups in the sense of Gromov. In the talk I will
give a survey of this area, and discuss the classification of
topological 4manifolds with such fundamental groups (joint work with
Matthias Kreck and Peter Teichner).


Michael Hutchings  
The embedded contact homology index revisited
We refine the relative grading on embedded contact homology
to an absolute grading which associates to each generator (a union of
Reeb orbits) a homotopy class of oriented 2plane fields. This is
obtained by modifying the contact plane field in a neighborhood of
each Reeb orbit in the union. If time permits, we will discuss how
this construction represents a (very small) step towards unifying
embedded contact homology with Heegaard Floer homology.


Mustafa Kalafat  
Topology of LCF 4Manifolds
We construct handlebody diagrams of families of nonsimply
connected Locally Conformally Flat(LCF)
4manifolds realizing rich topological types, which are obtained
from conformal compactifications of the 3manifolds, that are built
from the Panelled Web Groups. These manifolds have strictly negative
scalar curvature and the underlying topological 4manifolds do not
admit any Einstein metrics. This is a joint work with S. Akbulut.

