THIRTY-FIRST GÖKOVA
GEOMETRY / TOPOLOGY CONFERENCE
May 18 - May 23 (2026)
Gökova, Türkiye
List of invited speakers/participants
Russell Avdek
(Sorbonne U, France) | |
Sławomir Rams
(Jagiellonian U, Poland) | |
Zhengyi Zhou
(MCM, CAS, China) |
Tianyu Yuan
(EITech, China) | |
Alex Takeda
(Uppsala U, Sweden) | |
Elliot Gathercole
(Lancaster U, UK) |
Sergey Finashin
(METU, Türkiye) | |
Axel Husin
(RIMS, Kyoto U, Japan) | |
Yasemin Yıldırım
(Uppsala U, Sweden) |
| | |
Turgay Bayraktar
(Sabancı U, Türkiye)
| |
|
Scientific Committee : S. Akbulut, D. Auroux, E. Eftekhary, Y. Eliashberg, G. Dimitroglou Rizell, I. Itenberg, G. Mikhalkin, C. Taubes, U. Varolgüneş
Organizing Commitee : F. Arıkan, A. Degtyarev, S. Koçak, Y. Ozan, E. Z. Yıldız
Supported By: 
Santori Family Charitable Foundation  Selman Akbulut
The participants of 31st Gökova Geometry - Topology Conference
List of Talks
(Schedule)
 |
| Russell Avdek | |
Numerical invariants of contact manifolds and their divisors
I will introduce an invariant \( E(K)\) of \(codim = 2\) contact submanifolds \(K\) of a contact manifold (of any dimension),
generalizing the self-linking number \(SL(K)\) of transverse links in the contact \(3\)-sphere. Extending the observation that \(SL(L)=1\) \(mod\; 2\), modular properties \(E(K)\) are intimately related
to the divisibilities of certain Chern numbers. A generalization of Gompf's \(d3\) invariant is also defined and used to uncover surprising properties of \(E(K)\).
These tools provide novel information about Milnor numbers of complex hypersurface singularities.
| |
| Alex Degtyarev | |
A decade of line counting: an overview
I will give a brief overview of a long project that started a decade ago (in collaboration with Ilia Itenberg and Sinan Sertöz and in parallel with Slawomir Rams and Matthias Schütt)
and originally intended to bridge a minor gap in the proof of Segre's celebrated theorem on \(64\) lines on a smooth quartic surface.
Confining ourselves to polarized \(K3\)- surfaces, now we manage to answer questions that no one even dared to ask, mostly because of lack of tools. For example, we
• obtained sharp upper bounds on the possible number of lines on a smooth polarized \(K3\)-surface of any degree,
• obtained similar bounds for quartics, sextics, and octics with singularities,
• advanced in the understanding of conics on \(K3\)-surfaces (sharp upper bounds for quartics, sextics, and octics),
• started the study of twisted cubics.
I will try to discuss both classical (more than 5 years old) results and recent advances; if time permits, I will also try to outline the techniques used.
| |
| Georgios Dimitroglou Rizell | |
A survey of non-simplicity results for Legendrian twisted Whitehead doubles
Legendrian twisted Whitehead doubles have provided an important source of examples of non-simple Legendrian knot classes.
We give a survey of such results: first, the original Chekanov-Eliashberg knots, which where distinguished using Legendrian contact homology;
second, a more general family of twisted Legendrian Whitehead doubles of the unknot that were distinguished by Ozsvath-Stipsicz using Knot Floer Homology \((KFH)\);
finally, a very recent result by Kıvanç who used \(KFH\) to prove non-simplicity for a family of twisted Legendrian Whitehead doubles of the trefoil.
| |
| Sergey Finashin | |
Monodromy factorization of real elliptic Lefschetz fibrations of type \(E(1)\) and of their Real Mordell-Weil groups
After discussing generalities on the Real braids
and Real surface monodromy, I will review our joint work (in progress) with Mohan Bhupal on monodromy factorization of real pairs of sections of real Lefschetz fibrations,
\(X\), of type \(E(1)\). Such a pair defines a generator of the real Mordell-Weil group of \(X\).
On the other hand, such a pair defines a real plane quartic, whose braid monodromy factorization is covered by the monodromy factorization of \(X\) and is refined to the factorization of sections.
I plan to present a simple algorithm for construction the braid factorizations of Real quartics and the associated Real monodromy factorization of \(X\).
| |
| Elliot Gathercole | |
Superheavy skeleta from non-normal crossings divisors
A (smooth) complex Fano projective variety \(M\) is canonically a monotone symplectic manifold.
Given an effective anticanonical divisor \(D\), we obtain a choice of Liouville vector field on the complement of \(D\), which gives a retraction onto a
distinguished isotropic subset \(L\), the Lagrangian skeleton.
Superheaviness is a strong rigidity property of a closed subset of a symplectic manifold, which implies, in particular, non-displaceability by Hamiltonian isotopy.
In the case that \(D\) has singularities in a certain class, worse than normal crossings, we will describe a result establishing a sufficient numerical
condition on \(D\) for \(L\) to be a superheavy subset of \(M\). We will illustrate this with some interesting examples where the skeleton itself can be
shown to be superheavy, giving examples of rigid isotropic cell complexes which are not easily detected by Lagrangian Floer homology.
| |
| Axel Husin | |
Local systems and vanishing Maslov class
We present a new proof of the classical result that the Maslov class vanishes for closed exact
Lagrangians in cotangent bundles. Our approach uses Floer theory enriched with chains on Moore path spaces, building on work by Abouzaid and Barraud-Cornea.
We also explain how this framework extends to give vanishing results for the Maslov class of exact Lagrangians in slightly more general Weinstein domains.
This is joint work with Thomas Kragh and is available on arXiv:2410.01586.
| |
| Sławomir Rams | |
On large configurations of lines on some projective and affine complex surfaces
Configurations of lines on surfaces are a classical research subject,
with seminal results due to Cayley, Clebsch, Salmon and Monge to name a few. It is only within the last decade that our understanding of such configurations on complex
quartics (not necessarily smooth) became complete. In my talk I will discuss recent results on the subject. If time permits I will also present some results on
other rational curves/classes of surfaces (partially based on joint work with
A. Degtyarev, M. Schuett, T. Bauer and V. Gonzalez-Alonso).
| |
| Alex Takeda | |
(Pr)operadic algebraic structures from Poincaré duality
In this talk I will recall some non-commutative analogues of the notion of Poisson manifold,
which are described by algebras over certain algebraic structures called properads. I will describe how these structures can be produced starting from an object
with some type of orientation data, such as an oriented manifold, in the topological example, or a Weinstein manifold, in the symplectic setting.
The presence of these structures then gives rise to a rich set of algebraic operations on loop space homology/symplectic cohomology.
I will describe these structures and some conjectures about them. This talk is partly about joint work with M.Rivera, Z.Wang and C.Emprin.
| |
| Yasemin Yıldırım | |
Classification of Legendrian doubles and suspensions
We construct Legendrian submanifolds in contact manifolds obtained by doubling an exact
Lagrangian filling contained inside a page of an open book decomposition. The resulting objects, called Legendrian doubles, are shown to admit flexible, regular,
exact Lagrangian fillings, and are therefore classified up to Legendrian isotopy by their classical invariants. This generalizes a construction by Courte and Ekholm
which produced Legendrians doubles in the standard contact sphere from exact fillings in the ball.
Finally, we show that the Legendrian suspension constructed by Arıkan and the author in earlier work—this is a Legendrian contained inside a page of an open book
that is obtained by using Seidel’s suspension of Lefschetz fibrations—is a Legendrian double.
| |
| Tianyu Yuan | |
Orbifold Floer theory and Hecke algebras
Counting orbifold curves without abstract perturbation is usually difficult due to the collapse
of orbifold points. We generalize Doan-Walpuski's elimination of ghost bubbles to equivariant cases:
By explicitly computing the obstruction section, we show that forming certain orbifold ghost bubbles is a condition of at least real codimension two.
We also show that orbifold points approaching Lagrangian boundary corresponds to an equivariant skein relation, generalizing the \(HOMFLYPT\) skein relation considered
by Ekholm-Shende. As an application, the wrapped Fukaya category of a generic cotangent fiber of \(C^n/W\) is isomorphic to the
Hecke algebra of the complex reflection group \(W\). This is joint work with Honda, Krutowski and Tian.
| |
| Zhengyi Zhou | |
On symplectic \(CP^n\)
We show that the existence of a pseudo-holomorphic line passing through two generic points on a symplectic manifold \(X\),
phrased using Gromov-Witten invariants, implies that \(X\) is homotopy equivalent to \(CP^n\) with identical first Chern class and small quantum cohomology.
We then deduce some rigidity results regarding symplectic hyperplanes in \(CP^{n+1}\) as well as symplectic fillings. The proof is based on Rabinowitz Floer homology.
| |
|
|
Conference main page |
Last updated: May 2026
Web address: GokovaGT.org/2026
|
