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Bogazici UniversityTMD



Topology and geometry in low degrees

on the occasion of Sergey Finashin's 60th birthday

December 20-21, 2018

Istanbul, Turkey

This conference aims to bring experts together to discuss "topology and geometry in low degrees", on the occasion of Sergey Finashin's 60th birthday.


  • Mohan Bhupal (METU)
  • Çisem Güneş (Bilkent U)
  • Viatcheslav M. Kharlamov (U Strasbourg)
  • Grigory Mikhalkin (U Geneva)
  • Yıldıray Ozan (METU)
  • Nermin Salepci (U Lyon 1)
  • Özgür Kişisel (METU)
  • Eugenii Shustin  (Tel Aviv U)
  • Jean-Yves Welschinger (U Lyon 1)
  • Remziye Arzu Zabun (Gaziantep U)


                MFO Collection. Author: Ivonne Vetter, 2014. Photo ID: 19002. Modified.

Creative Commons License Attribution-Share Alike 2.0 Germany.


Scientific committee: Alex Degtyarev (Bilkent U), Ilia Itenberg (Inst Jussieu), Turgut Önder (METU), Ferit Öztürk (Boğaziçi U)

Organizing committee: Ferit Öztürk (Boğaziçi U), Remziye Arzu Zabun (Gaziantep U)




Detailed Program

Cisem Gunes Aktas (Abdullah Gul U) - Deformation Classes of Singular Quartic Surfaces

Abstract: In this talk we discuss the problem of classifying quartic surfaces with simple singularities up to equisingular deformations. Simple quartics are K3- surfaces and as such they can be studied by means of the global Torelli theorem and the surjectivity of the period map combined with Nikulin's theory of discriminant forms. We reduce the classification problem to a certain arithmetical problem concerning lattice extensions. Then, based on Nikulin's existence criterion, we list all sets of simple singularities realized by the non-special quartics. For each realizable set of singularities, we use Miranda-Morrison's theory to give a complete description of the connected components of the corresponding equisingular stratum. We also develop an algorithm detecting real representatives in equisingular strata of projective models of K3-surfaces. We apply this algorithm to spatial quartics and find two new examples of real strata without real representatives.

Mohan Bhupal (METU) - Open books decompositions of links of minimally elliptic singularities

Abstract: I will discuss some results that allow one to obtain an explicit Milnor open book decomposition supporting the canonical contact structure on the link of any minimally elliptic singularity whose fundamental cycle Z satisfies −3 ≤ Z ⋅ Z ≤ −1.

Viatcheslav Kharlamov (U Strasbourg) - Selected open problems form joint works with Sergey Finashin

Abstract: The aim of the talk is to overfly results obtained and to discuss certain problems that they put forward. The aim of the talk is a brief overview of the results obtained and a discussion of certain problems that they put forward.

Ozgur Kisisel (METU) - Real and Complex Line Arrangements

Abstract: There are many natural problems of interest concerning the arrangement of lines in the real or complex projective plane related to the combinatorial properties of the resulting cell complex. In this talk I first wish to introduce some of these problems and some recent developments about them. Finally, I will present certain realizability results about a certain subclass of line arrangements, called nets, that we obtained in our joint work with A. Bassa.

Grigory Mikhalkin (U Geneva) - Lagrangian manifolds and tropical curves

Abstract: Consider the following symplectic counterpart of the 16-th Hilbert problem in higher dimension: given a closed symplectic manifold X, list all possible Lagrangian manifolds L inside X. There are several versions to this question: e.g. we may be interested only in the possible topology of L, or in L up to Hamiltonian isotopy of X. The submanifold L may well be disconnected, or we may also allow L to have some singularities. As in real algebraic geometry, there are two parts in attacking this problem: constructions and prohibitions. Through a symplectic adaptation of Viro's patchworking technique, tropical curves can be used for constructions. Furthermore, in a number of situations, tropical curves can also be used in the context of Symplectic Field Theory (in the sense of Eliashberg-Givental-Hofer) to obtain some prohibitions through enumerative geometry. In the talk we'll survey some first results in these directions.

Yildiray Ozan (METU) - A Filtration on the Borel-Moore Homology of the Wonderful Compactification of some Symmetric Spaces

Abstract: Let X be the wonderful compactification of a symmetric homogeneous variety G/H, where rk(G) = rk(H). We will construct a filtration on the Borel-Moore homology on X, as a graded module, with the associated graded module equal to the direct sum of Borel-Moore homology groups of the G-orbits in X.

Nermin Salepci (U Lyon 1) - Lower estimates for the expected Betti numbers of random subcomplexes in a finite simplicial complex

Abstract: We consider a finite simplicial complex K together with d-th barycentric subdivisions and study the expected topology of a random subcomplex in subdivided complex. In this talk, we will present asymptotic lower bounds for the expected Betti numbers of these subcomplexes. This is a joint work with J.-Y. Welschinger.

Eugenii Shustin (Tel Aviv U) - Refined enumeration of elliptic curves in toric surfaces

Abstract: Following Mikhalkin's ideas, we consider the problem of enumeration of real elliptic curves in toric surfaces that have fixed real tangency points of even multiplicity with toric divisors and pass through a fixed real point in the big torus. All counted curves are M-curves and possess a quantum index in the sense of Mikhalkin. First, we show that under certain mild restrictions to the toric surface, the Welschinger-type count of real elliptic curves of a given degree and quantum index is invariant with respect to the variation of constraints. Second, we show that the corresponding enumeration of plane tropical elliptic curves admits a refinement, while the refined tropical invariant after some normalization coincides with the algebraic refined invariant. Third, we suggest a recursive formula computing the rational and elliptic refined invariants of the considered type. Joint work with I. Itenberg.

Jean-Yves Welschinger (U Lyon 1) - Tilings, packings and expected Betti numbers in simplicial complexes

Abstract: I will explain how to bound from above the expected Betti numbers of a random subcomplex in a simplicial complex. I will then explain how packings of simplices make it possible to improve these upper bounds and finally discuss a notion of tilings which makes it possible to produce such packings. This is a joint work with Nermin Salepci.

Remziye Arzu Zabun (Gaziantep U) - Cremona Transformations of Plane Configurations of 6 Points

Abstract: This talk is based on a study of the behavior of 6-points con gurations under plane Cremona transformations. As an application, we give an alternative approach to determining the deformation types (i.e., icosahedral, bipartite, tripartite and hexagonal) of 36 real Schlafli double sixes on any non-singular real cubic surface performed by Segre.


If you have any questions or comments, please do not hesitate to contact the organizers Ferit Öztürk  and Remziye Arzu Zabun.