GEOMETRY / TOPOLOGY CONFERENCE
May 28 - June 2 (2012)
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
The participants of 19th Gökova Geometry - Topology Conference
List of Talks
| Cagatay Kutluhan ||
|| Lectures on the equivalence of Heegaard Floer and Seiberg-Witten Floer homologies (mini course) |
The goal of these lectures is to explain the construction of an isomorphism between Heegaard Floer and Seiberg-Witten Floer homologies in joint work with Yi-Jen 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 Strominger-Yau-Zaslow Mirror Conjecture and recent progress in toric cases.
An informal talk on G2
| 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 An. We next study some finite quotients of the An
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 An 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 An
Milnor fibre. We conclude that these Stein surfaces have non-vanishing
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 finite-dimensional model: Morse homology (and the Morse category) of a manifold with boundary.
A bordered monopole Floer theory
I will report on work-in-progress to develop a bordered monopole Floer theory. We associate an algebra to a surface, a module to 3-manifold with boundary, and a map of modules to a 4-manifold with corners (all in the A-infinity sense). These structures satisfy the natural gluing theorems inherent in a 4-dimensional 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 Juhász in Heegaard Floer homology. Contact 3-manifolds 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 2-algebra. I will also discuss a decomposition theorem for bordered modules associated to nice diagrams, corresponding to cutting a 3-manifold 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 self-similar and graph-directed fractals.
| Cagri Karakurt ||
|| Corks and exotic smooth structures of 4-manifolds |
It is known that any two simply connected homotopy equivalent closed smooth 4-manifolds differ by a surgery along a contractible codimension 0 sub-manifold so-called cork. Understanding gauge theoretical properties of corks play a crucial role in smooth classification of 4-manifolds. In this talk I will present a joint work with S. Akbulut on calculation of
relative Ozsvath-Szabo invariants of an infinite family corks.
| Kenta Hayano ||
|| Modification rule of monodromies in R2-move |
An R2-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 4-manifolds by simple
closed curves in closed surfaces.
| Max Lipyanskiy ||
|| Gromov-Uhlenbeck Compactness |
We introduce an analytic framework that, in special circumstances, unites Yang-Mills 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 4-manifolds |
Any smooth, closed oriented 4-manifold 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 3-manifolds |
In this talk, we study the genus of absolutely area minimizing surfaces in a compact, orientable, strictly mean convex 3-manifold M, and give several results on minimal surfaces in mean convex 3-manifolds. This is a joint work with Theodora Bourni.
| Selman Akbulut ||
|| Twisting 4-manifolds along surfaces |
Given an imbedding of Fg ⊂ M4, where Fg 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 Fg
(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 n-dimensional 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.