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

FIFTEENTH GÖKOVA
GEOMETRY / TOPOLOGY CONFERENCE

May 26 - May 31 (2008)
Gökova, Turkey

List of invited speakers and participants

L.Ng       P.Lu       T.Etgu
P.Rossi       R.Lipshitz       I.Hambleton
M.Hutchings       C.Karakurt       E.Brugalle
I.Baykur       Y-T.Siu       A.Akhmedov
Y.Lekili      N.Salepci       O.Kisisel
B.Coskunozer       O.Ceyhan       M.Bhupal
B.Ozbagci       S.Salur       M.Kalafat

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 15th Gökova Geometry - Topology Conference

List of Talks
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 mini-course 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 three-space.
Anar Akhmedov    Stein fillings of contact manifolds
We give an infinite family of examples of contact three-manifolds 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 3-manifolds 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 one-to-one correspondence between isomorphism classes of partial open book decompositions modulo positive stabilization and isomorphism classes of compact contact 3-manifolds with convex boundary.
Çagri Karakurt    Every 4-Manifold is BLF
I will outline the proof that every compact smooth 4-manifold X has a structure of a Broken Lefschetz Fibration (BLF in short). Furthermore, if b2+(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 4-dimensional handlebody theory (this is a joint work with S. Akbulut).
Yanki Lekili    Wrinkled fibrations on near-symplectic manifolds
Motivated by the programmes initiated by Taubes and Perutz, we study the geometry of near-symplectic 4-manifolds 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 4-manifolds.
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 3-manifolds. Specifically, using the conformally invariant Cotton tensor on a 3-manifold, 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 Chern-Simons 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 3-sphere 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 P1-orbifolds and reflection groups of type ADE
Symplectic Field Theory in the target orbifold situation allows us to compute the Gromov-Witten 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 P1-orbifolds 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.
Yum-Tong Siu    Techniques and problems in application of d-bar estimates to algebraic geometry
I will explain the key arguments in the application of d-bar 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 S2 together with a real structure and study the real locus (which is a fibration over S1) 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 S1 which leads to a combinatorial object which we call necklace diagrams. Using necklace diagrams we obtain a classification of real elliptic Lefschetz fibrations over S2 with only real critical values. This classification gives the real analogue of the well-known 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 2-complexes and 4-manifolds
There is a rich class of finitely presented groups which occur as fundamental groups of aspherical 2-complexes. Examples include 1-relator groups (e.g. Baumslag-Solitar 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 4-manifolds 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 2-plane 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 4-Manifolds
We construct handlebody diagrams of families of non-simply connected Locally Conformally Flat(LCF) 4-manifolds realizing rich topological types, which are obtained from conformal compactifications of the 3-manifolds, that are built from the Panelled Web Groups. These manifolds have strictly negative scalar curvature and the underlying topological 4-manifolds do not admit any Einstein metrics. This is a joint work with S. Akbulut.
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Last updated: June 2008
Wed address: GokovaGT.org/2008