List of invited speakers/participants (tentative)
| F. Bogomolov | |
B. Khesin | |
I. Cheltsov |
| I. Zharkov | |
V. Fock | |
N. A'Campo |
| D. Matessi | |
E. Lupercio | |
J. Welschinger | |
| S. Orevkov | |
W. Chen | |
R. Golovko | |
| Ü. Yıldırım | |
H. Argüz | |
S. Arkhipov | |
| N. Sağlam | |
E. Yıldız | |
W. Czerniawska | |
| I. Fesenko | |
S. Finashin | |
M. Bhupal | |
| A. Bassa | |
| |
T. Bayraktar | |
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, S. Salur, F. Arıkan
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| Roman Golovko | |
On Legendrian products and twist spuns
The Legendrian product of two Legendrian knots, as defined by Lambert-Cole, is a Legendrian torus. We show that this Legendrian torus is a twist spun whenever one of the Legendrian knot components is sufficiently large. We then study examples of Legendrian products which are not Legendrian isotopic to twist spuns. In order to do this, we prove a few structural results on the bilinearised Legendrian contact homology and augmentation variety of a twist spun. In addition, we show that the threefold Bohr-Sommerfeld covers of the Clifford torus and Chekanov torus are not twist spuns. This is joint work with Georgios Dimitroglou Rizell. |
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| Fedor Bogomolov | |
Mini Course (2 Lectures): On the base of a lagrangian fibration for a compact hyperkahler manifold
In my talk I will discuss our proof with N. Kurnosov that the base of such fibration for complex projective manifold hyperkahler manifold of dimension \(4\) is always a projective plane \(\mathbb P^2\). In fact we show that the base of such fibration can not have a singular point of type \(E_8\). It was by the theorem of Mtasushita and others that only quotient singularities can occur and if the base is smooth then the it is isomorphic to \(\mathbb P^2\). The absence of other singualrities apart from \(E_8\) has been already known and we show that \(E_8\) can not occure either. Our method can be applied to other types of singularities for the study of lagrangian fibrations in higher dimensions. More recently similar result was obtained by Huybrechts and Xu. |
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| Boris Khesin | |
Mini Course (2 Lectures): Pentagram maps on space polygons and the Boussinesq evolution of curves
We describe pentagram maps on polygons in any dimension, which extend R.Schwartz's definition of the 2D pentagram map. Many of those maps turn out to be discrete integrable dynamical systems, while the corresponding continuous limits of such maps coincide with equations of the KdV hierarchy on space curves, generalizing the Boussinesq equation in 2D. We discuss their geometry and interrelations between several recent pentagram generalizations. |
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| Nur Saglam | |
Constructions of Lefschetz Fibrations via Cyclic Group Actions
We construct families of Lefschetz fibrations over \(\mathbb{S}^2\) using finite order cyclic group actions on the product manifolds \(\Sigma_{g} \times \Sigma_{g}\) for \(g>0\). We also obtain more families of Lefschetz fibrations by applying the rational blow-down operation to these Lefschetz fibrations. This is joint work with Anar Akhmedov. |
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| Vladimir Fock | |
Tau-function on Riemann surfaces
Tau-functions of Sato are certain generating functions for solution of integrable PDE like KdV, Sine-Gordon etc. There are many versions of these functions and usually the definition is quite complicated and uses semi-infinite forms. We are going to give a simple definition for a tau-function as an algebro-geometric object and show its relation to cluster varieties. |
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| Ilia Zharkov | |
Тopological SYZ fibrations: discriminant in cоdimension 2
In all known constructions of the torus fibrations of Calabi-Yau manifolds the discriminant locus on the base is of codimension 1 (except the trivial case of K3 and the quintic threefold, due to M. Gross). In a joint project (in progress) with Helge Ruddat we try to show how to make it of codimension 2 for a fairly large class of examples. |
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| Diego Matessi | |
On homological mirror symmetry of toric Calabi-Yau manifolds
I will report on joint work with M. Gross where we construct a large number of Lagrangian spheres inside the mirror of a toric (open) Calabi-Yau manifold. We formulate a precise correspondence between these spheres and sheaves supported on toric divisors of the toric Calabi-Yau and we conjecture that this correspondence should be induced by an equivalence of the Fukaya category and the derived category of coherent sheaves. Following recent work of Mikhalkin, Hicks and myself, I will also speculate on the possiblity of enriching this correspondence with tropical Lagrangian submanifolds. |
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| Ivan Cheltsov | |
Mini Course (2 Lectures): Borisov-Alexeev-Borisov conjecture and its applications
In this talk, I will describe Borisov-Alexeev-Borisov conjecture about boundedness of the set of Fano varieties with mild singularities, which was recently proved by Caucher Birkar. I will explain why it was not easy to prove it and present its applications in Birational Geometry. |
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| Ernesto Lupercio | |
Self Organized Criticality and Tropical Geometry
In this talk I will explain how to apply tropical geometry to obtain a continuous model for self-organized criticality. |
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| Stepan Orevkov | |
On Hurwitz equivalence of braid monodromies
A braid monodromy of a plane complex algebraic curve with respect to a pencil of lines is the natural homomorphism of the fundamental group of the complement to the singular fibers (which is a free group) to the braid group. Another braid group act on the free group by diffeomorphisms of the pencil (the so-called Hurwitz action). The talk is devoted to the following algorithmic problems: (1) to recognize Hurwitz-equivalent braid monodromies; (2) to find representatives of all orbits. I am going to present a solution to these problems for 3-braids under some additional restrictions. As an application we obtain a series of new quasipositivity tests for 4-braids. Some results of the talk are joint with Alexey Muranov. |
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| Ivan Fesenko | |
Adelic bridges between geometry and analysis on elliptic surfaces
For an elliptic surface (with zero section), the Tate-Birch-Swinnerton-Dyer formula conjecturally relates the analytic rank of its zeta function at the central point with its Picard rank. While existing approaches to this famous conjecture typically concentrate on one of fibres on the surface, I will talk about the higher adelic approach which involves full geometry and arithmetic of the surface, divisors and zero-cycles. It lifts the two discrete invariants to adelic invariants on the surface and relates the latter using topoloical self-duality of two complete adelic structures on the surface. |
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| Jean-Yves Welschinger | |
Tiles and tilings in simplicial geometry
I will introduce a notion of tilings in the simplicial category and discuss its relations with h-vectors, a packing problem and Morse theory. This is a joint work with Nermin Salepci. |
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| Hülya Argüz | |
Tropical real enumerative geometry and toric degenerations
Tropical geometry builds a computationally effective framework to study enumerative problems in real algebraic geometry. In particular, in the study of Welschinger invariants, tropical methods have seen rapid development, starting with fundamental results proved by Mikhalkin, and more recently in the case of non-toric del Pezzo surfaces by Itenberg--Kharlamov--Shustin. In this talk, we discuss a tropical correspondence theorem for real curves in toric degenerations. For this, we use log geometric tools and the degeneration approach of Nishinou--Siebert, which potentially give rise to tropical computations of real invariants in more general non-toric situations. This talk reports on joint work in progress with Pierrick Bousseau. |
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| Sergey Arkhipov | |
Derived Hamiltonian reduction and representations of the derived loop group
Given an algebraic group \(G\) acting on an algebraic variety \(X\), we interpret the derived category of coherent sheaves on the Hamiltonian reduction of the cotangent bundle to \(G\) in terms of representations of the group of derived loops with values in \(G\). |
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| Eylem Zeliha Yıldız | |
Knot Concordances in 3-Manifolds and Exotic Smooth 4-Manifolds
We will discuss some notions of knot concordances in 3-manifolds and related recent results. In particular we will prove that any knot in \(S^1 \times S^2\), which is freely homotopic to \(S^1 \times pt\), is invertibly concordant to \(S^1 \times pt\). In the second part of the talk, we will show how to construct Akbulut-Ruberman type exotic manifolds using the invertible concordances that we construct in the first part. This is a joint work with Selman Akbulut. |
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