TWENTY-THIRD GÖKOVA
GEOMETRY / TOPOLOGY CONFERENCE
May 30 - June 4 (2016)
Gökova, Turkey
List of invited speakers/participants
| M. Verbitsky | |
T. Walpuski | |
G. Tian |
| S. Galkin | |
T. Vogel | |
U. Varolgunes |
| V. Shende | |
S. Borman | |
M. Can | |
| P. Ghiggini | |
R. Golovko | |
S. Finashin |
| M. Bhupal | |
M. Kalafat | |
B. Coskunuzer |
| T. Dereli | |
G. Tinaglia | |
C. Karakurt |
| I. Unal | |
S. Uguz | |
F. Ozturk |
Scientific Committee : D. Auroux, Y. Eliashberg, I. Itenberg, G. Mikhalkin, S. Akbulut, A. Oancea
Organizing Commitee : T. Önder, S. Koçak, A. Degtyarev, Ö. Kişisel, Y. Ozan, T. Etgü, S. Salur
Supporting Organizations: NSF (National Science Foundation),
and
TMD (Turkish Mathematical Society)
and
ERC (European Research Council).
The participants of 23rd Gökova Geometry - Topology Conference
List of Talks
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| Gang Tian | |
Gauged Witten equation and its application
This talk is based on my recent papers joint with Guangbo Xu. I will first introduce the gauged Witten equation which generalizes the symplectic vortex equation. Next, I will discuss some analytical aspects of this equation, including the Fredholm property and the compactness. In the end, I will explain how to construct the gauged linear σ-model invariants by using the gauged Witten equation and the virtual technique Li-Tian used. These invariants provide a connection between the σ-models on Calabi-Yau manifolds and the Landau-Ginzburg models.
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| Misha Verbitsky | |
Mini course: Ergodic theory of mapping group action and moduli spaces
The Teichmuller space of geometric structures of certain
type is the quotient of the set of all geometric structures
of this type by the group of isotopies (that is, the connected
component of the diffeomorphism group). The natural
examples are Teichmuller spaces of complex, symplectic,
holomorphically symplectic, hyperkahler or holonomy
G2 structures; they are all finite-dimensional
and often smooth manifolds. I will focus on the Teichmuller
space of symplectic structures, which is a smooth,
finite-dimensional manifold, and describe it explicitly
for hyperkahler manifolds, such as K3 surface and
a torus. I will explain the ergodic properties of
the mapping group action on the symplectic
Teichmuller space, and give some applications.
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Mini course: Full symplectic packing for hyperkähler manifolds and tori
Let M be a compact symplectic manifold
of volume V. We say that M admits a full
symplectic packing if for any collection S
of symplectic balls of total volume less than
V, S admits a symplectic embedding to M.
In 1994, McDuff and Polterovich proved that
symplectic packings of Kähler manifolds can
be characterized in terms of Kähler cones of
their blow-ups. When M is a Kähler manifold
which is not a union of its proper subvarieties
(such a manifold is called simple) these Kähler
cones can be described explicitly using Demailly
and Paun structure theorem.
It follows that any simple Kähler manifold admits
a full symplectic packing. This is used to show
that compact tori and hyperkähler manifolds admit a
full symplectic packing. This is a joint work
with Michael Entov. I would also formulate some
results about full packing by other shapes,
and ask questions relating symplectic packing and
ergodic theory.
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| Thomas Walpuski | |
Mini course: G2 geometry
One of the basic invariants of a Riemannian manifold is its holonomy group. According to Berger’s classification one distinguishes four special holonomy groups, corresponding to Kähler, Calabi–Yau, quaternionic Kähler, and hyperkähler geometry, as well as two exceptional holonomy groups: G2 and Spin(7). The focus of this mini course is on G2 geometry (the most exceptional of the geometries). We will learn about the most common ways to think about G2–manifolds, their basic topological and metric properties, obstructions to the existence of G2–structures, and construction methods—in particular, about the twisted connected sum construction; as well as about moduli spaces of G2–manifolds, and the role of calibrated geometry and gauge theory in G2 geometry.
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| Vivek Shende | |
The conormal torus is a complete knot invariant
We show that if two links have Legendrian isotopic collections of conormal tori, then the links are isotopic or mirror images. The argument uses sheaf quantization, and also appeals to left-orderability of link groups. I will begin with some introductory material on constructible sheafs.
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| Thomas Vogel | |
Non-loose unknots in S3
We discuss Legendrian unknots in S3 carrying an overtwisted contact
structures such that the complement of the unknot is tight. In this
situation, despite of Eliashberg's classification theorem, rigidity
phenomena appear.
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Old and new results on Engel structures
This is a survey talk on Engel structures and known existence
results (an older result be the speaker and a new theorem by Casals,
Perez, del Pino, Presas). We will also state some of the main open
questions.
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| Mahir Bilen Can | |
Complex G2 and associative grassmanian
The associative grassmannian is a central object in the study of Harvey-Lawson manifolds.
It turns out, over the field of complex numbers, this variety is the unique smooth spherical compactification of G2/SO(4) with Picard number 1.
In this talk we are going to give a detailed analysis of the geometry of associative grassmannian and report our more recent results on its relatives
(including a smooth compactification of G2/SO(3)).
This is based on our joint work with Selman Akbulut.
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| Umut Varolgüneş | |
On the equatorial Dehn twist of a two dimensional nodal Lagrangian sphere
Let S be a strongly exact nodal Lagrangian sphere with exactly one transverse self intersection at the two "poles" inside an exact four dimensional symplectic manifold X. Let us denote by φ the automorphism of S given by a Dehn twist around an "equatorial" curve. We show that there is no Hamiltonian diffeomorphism of X, fixing S setwise, that realizes φ. The proof uses higher structures in the Lagrangian Floer theory of S in an essential way. We derive inspiration from our partial understanding of mirror symmetry for the symplectic manifold which is the standard Weinstein neighborhood of such a nodal Lagrangian sphere. The result itself can be seen as a continuation of Lalonde-Hu-Leclercq's result about the same question for embedded exact Lagrangian submanifolds, which says that a diffeomorphism of the submanifold that can be realized by an ambient Hamiltonian diffeomorphism has to act trivially on cohomology. We also strengthen this result on the way.
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| Sergey Galkin | |
Hyperkähler manifolds and mirror symmetry
Kähler manifolds with special holonomy and polarization by a lattice of integral Kähler cycles come in mirror dual families.
I will speak of what is known and expected about natural one-dimensional families of hyperkähler manifolds and their mirror duals,
with a couple of explicit examples and conjectures.
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| Paolo Ghiggini | |
Noncommutative augmentation categories
To a differential graded algebra with coefficients in a noncommutative algebra, by dualisation we associate an A∞ category whose objects are augmentations. This generalises the augmentation category of Bourgeois and Chantraine (and subsequent generalisations of it) to the noncommutative world.
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| Matthew Strom Borman | |
Overtwisted contact structures
The notion of an overtwisted contact 3-manifold and its associated h-principle has been a central part of contact topology for the last twenty-five years. In joint work with Eliashberg and Murphy, we generalized the notion of an overtwisted contact structure to higher dimensions and proved the corresponding h-principal. In this talk I will give an overview of the proof of the h-principle for overtwisted contact structures in higher dimensions.
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