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INVITED SPEAKERS:
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Creative Commons License Attribution-Share Alike 2.0
Germany. |
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COMMITEES: 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) |
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SCHEDULE: 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.
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CONTACT
US:
If you have any
questions or comments, please do not hesitate to contact the organizers Ferit Öztürk and Remziye Arzu Zabun. |
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