NINETEENTH GÖKOVA GEOMETRY / TOPOLOGY CONFERENCE
May 28  June 2 (2012)
Gökova, Turkey
List of invited speakers/participants
M. Lipyanskiy  
C. Leung  
C. Kutluhan 
G. Mikhalkin  
J. Bloom  
R. Kirby 
Y. Lekili  
F. Arikan  
C. Karakurt 
S. Kocak  
J. Williams  
S. Sivek 
C. Manolescu  
S. Salur  
B. Ozbagci 
K. Hayano  
I. Baykur  
M. Kalafat 
S. Finashin  
S. Durusoy  
O. Kisisel 
Scientific Committee : D. Auroux, Y. Eliashberg, I. Itenberg, G. Mikhalkin, S. Akbulut
Organizing Commitee : T. Önder, S. Koçak, A. Degtyarev, M. Korkmaz, Y. Ozan, T. Etgü, B.Coskunuzer
Supporting Organizations: NSF (National Science Foundation) and
TUBITAK.
The participants of 19^{th} Gökova Geometry  Topology Conference
List of Talks

Cagatay Kutluhan  
Lectures on the equivalence of Heegaard Floer and SeibergWitten Floer homologies (mini course)
The goal of these lectures is to explain the construction of an isomorphism between Heegaard Floer and SeibergWitten Floer homologies in joint work with YiJen Lee and Clifford H. Taubes. We will provide some background, describe the ingredients in our construction, and give an outline of the proof of the equivalence.


Conan Leung  
SYZ Mirror Symmetry
In this talk I will explain the StromingerYauZaslow Mirror Conjecture and recent progress in toric cases.
An informal talk on G_{2}


Yanki Lekili  
Floer theoretically essential tori in rational blowdowns
We compute the Floer cohomology of monotone tori in the Stein
surfaces obtained by a linear plumbing of cotangent bundles of spheres,
also known as the Milnor fibre associated with the complex surface
singularity of type A_{n}. We next study some finite quotients of the A_{n}
Milnor fibre which coincide with the Stein surfaces that appear in
Fintushel and Stern's rational blowdown construction. We show that these
Stein surfaces have no exact Lagrangian submanifolds by using the
already available and in depth understanding of the Fukaya category of
the A_{n} Milnor fibre coming from homological mirror symmetry. On the
contrary, we find Floer theoretically essential monotone Lagrangian
tori, finitely covered by the monotone tori that we studied in the A_{n}
Milnor fibre. We conclude that these Stein surfaces have nonvanishing
symplectic cohomology. Joint work with Maksim Maydanskiy.


Jonathan Bloom  
Morse (and Floer) homology with boundary
Extending the TQFT structure of monopole Floer homology is complicated by the fact that the configuration space has boundary (the reducibles).
We show how to package the cobordism relations among the resulting moduli spaces into algebraic structure, using a notion of path DGA on a directed hypergraph. Our approach is motivated by, and applies to, the finitedimensional model: Morse homology (and the Morse category) of a manifold with boundary.
A bordered monopole Floer theory
I will report on workinprogress to develop a bordered monopole Floer theory. We associate an algebra to a surface, a module to 3manifold with boundary, and a map of modules to a 4manifold with corners (all in the Ainfinity sense). These structures satisfy the natural gluing theorems inherent in a 4dimensional TQFT with corners, and are closely related to Khovanov's invariant of tangles and Szabo's geometric spectral sequence. This is joint work with John Baldwin.


Steven Sivek  
A contact invariant in sutured monopole homology
Kronheimer and Mrowka recently used monopole Floer homology to define an invariant of sutured manifolds, following work of JuhĂˇsz in Heegaard Floer homology. Contact 3manifolds with boundary are natural examples of such manifolds. In this talk, I will construct an invariant of a contact structure as an element of the associated sutured monopole homology group. I will discuss several interesting properties of this invariant, including gluing maps which are analogous to the Heegaard Floer sutured gluing maps of Honda, Kazez, and Matic, and a bypass exact triangle relating the homology groups for different choices of sutures. This is joint work with John Baldwin.


Ciprian Manolescu  
The Heegaard Floer invariant of the circle
As part of the bordered Floer homology package, Lipshitz, Ozsvath and D. Thurston have associated to a parametrized oriented surface a certain differential graded algebra. I will describe a decomposition theorem for this algebra, corresponding to cutting the surface along a circle. In this decomposition, we associate to the circle a categorical structure called the nilCoxeter sequential 2algebra. I will also discuss a decomposition theorem for bordered modules associated to nice diagrams, corresponding to cutting a 3manifold with boundary along a surface transverse to the boundary. This is joint work with Christopher Douglas.


Sahin Kocak  
Tube Formulas for Fractals
After giving a brief review of classical results on tubes of convex subsets and submanifolds of Euclidean spaces, I will explain the recent developments on tubes of selfsimilar and graphdirected fractals.


Cagri Karakurt  
Corks and exotic smooth structures of 4manifolds
It is known that any two simply connected homotopy equivalent closed smooth 4manifolds differ by a surgery along a contractible codimension 0 submanifold socalled cork. Understanding gauge theoretical properties of corks play a crucial role in smooth classification of 4manifolds. In this talk I will present a joint work with S. Akbulut on calculation of
relative OzsvathSzabo invariants of an infinite family corks.


Kenta Hayano  
Modification rule of monodromies in R_{2}move
An R_{2}move is a homotopy whose variants are contained in
several important deformations of wrinkled fibrations. In this talk,
we first show how monodromies of a fibration are changed by this
move. As an application, we then give several examples of diagrams which
were introduced by Williams to describe smooth 4manifolds by simple
closed curves in closed surfaces.


Max Lipyanskiy  
GromovUhlenbeck Compactness
We introduce an analytic framework that, in special circumstances, unites YangMills theory and the theory of pseudoholomorphic curves. As an application of these ideas, we discuss the relation between instanton Floer homology and Lagrangian Floer homology of representation varieties.


Jonathan Williams  
Surface diagrams of smooth 4manifolds
Any smooth, closed oriented 4manifold M has a surface diagram, which is a closed, orientable surface, decorated with simple closed curves, that specifies M up to diffeomorphism. I will discuss various properties of surface diagrams.


Baris Coskunuzer  
Area minimizing surfaces in mean convex 3manifolds
In this talk, we study the genus of absolutely area minimizing surfaces in a compact, orientable, strictly mean convex 3manifold M, and give several results on minimal surfaces in mean convex 3manifolds. This is a joint work with Theodora Bourni.


Selman Akbulut  
Twisting 4manifolds along surfaces
Given an imbedding of F_{g} ⊂ M^{4}, where F_{g} is a surface of genus g,
I will discuss the question of when (and if) you get an exotic copy of M by twisting M along F_{g}
(when g=0 this operation is called Gluck twisting). In particular, I will discuss a recent theorem about Gluck twisting proved jointly with Yasui.


Sergey Finashin  
Abundance of real lines
A generic real projective ndimensional hypersurface of degree 2n  1 contains
many real lines, namely not less than (2n  1)!!, which is approximately the square
root of the number of complex lines. This estimate is based on the interpretation of a
suitable signed count of the lines as the Euler number of appropriate bundles.


