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Eugenii Shustin
Title: Examples of real algebraic and tropical enumerative invariants
Abstract: We present a series of new examples of real enumerative invariants counting real rational curves on real del Pezzo surfaces. Some of them admit tropical analogs defined for arbitrary toric surfaces and for arbitrary genus.
Lionel Lang
On approximation of harmonic tropical curve.
The generalization of the amoeba map introduced by I.Krichever suggest the consideration of a wider class of tropical curves, with non rational slopes. To be more precise, it suggest a generalization of the notion of tropical morphism from abstract tropical curves to R^n. Both generalization of amoebas and immersed tropical curve will be called harmonic. After motivating the terminology, we will see how one can approximate any harmonic tropical curve by a family of harmonic amoebas. With a bit of extra work, it gives an “alternative” proof to Mikhalkin's theorem on approximation of complex tropical curves in the plane.
Karim Adiprasito
Title: Tropical Lefschetz theorems and filtered geometric lattices
Abstract: I will review some analogues of the classical Lefschetz Section Theorem for smooth tropical varieties. More precisely, I will present tropical analogues of the section theorems of Lefschetz, Andreotti-Frankel, Bott-Milnor-Thom, Hamm-L{\^e} and Kodaira-Spencer, and the vanishing theorems of Andreotti-Frankel and Akizuki-Kodaira-Nakano. We start the paper by resolving a conjecture of Mikhalkin and Ziegler (2008) concerning the homotopy Cohen-Macaulayness of certain filtrations of geometric lattices, generalizing earlier work on full geometric lattices by Folkman and others.
Ilia Itenberg
tba
Ludmil Katzarkov
Categorical base loci and applications
We introduce the notion of categorical base loci. Possible applications will be considered.
Sergey Galkin
Title: Polynomial relations between holomorphic curves and discs
Abstract: I will tell about polynomial relations between numbers of pseudo-holomorphic curves, passing through a point, and numbers of pseudo-holomorphic discs, bounded on some Lagrangian torus. The relations comes from a comparison of different pictures of mirror symmetry, and can be proved only using tropical geometry (so far).
Hannah Markwig
Tropicalizing rational relative Gromov-Witten theory of P^1
abstract: We show that the relative stable map compactification of M_0,n (for maps to P^1, relative to two points) is a tropical compactification. Furthermore, the tropicalization of the open part equals the tropical space of relative stable maps to P^1. Consequently, the Chow ring of the relative stable map space can be computed by means of tropical intersection theory in an intuitive way. This is joint work with Renzo Cavalieri and Dhruv Ranganathan.
Luis-Felipe Tabera
Title: Singular tropical hypersurfaces in positive characteristic.
Abstract: In this talk I will consider tropical varieties as non-archimedean amoebas defined over fields in positive characteristic. I will define a tropical singularity and give a method to compute the singular locus of a tropical hypersurface in positive characteristic. As a consequence, I will describe some cells of the discriminant in characteristic p. I will briefly mention the case of the p-adics and we will see that the p-adic tropical discriminant is an “interpolation” of the tropical discriminants in characteristic 0 and p.
Takeo Nishinou
Degeneration and curves on K3 surfaces.
There is a well-known conjecture which states that all projective K3 surfaces contain infinitely many rational curves. By calculating obstructions in deformation theory through degeneration, we give a new approach to this problem. In particular, we show that there is a Zariski open subset in the moduli space of projective complex K3 surfaces whose members fulfil the conjecture.
Erwan Brugalle
tba
Tony Yue Yu
tba
Ilia Zharkov
Building skeleta of affine surfaces