Prochains séminaires
Lundi 22 Septembre 2014, 15h00, Villa Battelle
Mikhail Shkolnikov (Geneve)
I will review some recent results on hyperbolic amoebas and explain how they are related to constant mean curvature surfaces in hyperbolic 3-space.
Jeudi 22 Mai 2014, 13h00, Villa Battelle
Johannes Josi (Geneve)
An idea to present a classical Lie group of positive dimension by
generators and relations sounds dubious, but happens to be fruitful. The
isometry groups of classical geometries admit elegant and useful
presentations by generators and relations closely related to geometry.
They allow to make fast and efficient geometric calculations. In this
paper simple presentations of the isometry groups of Euclidean plane,
2-sphere, the real projective plane and groups SO(3), O(n) are introduced.
Lundi 23 decembre 2013, 14h30, Villa Battelle
Nikita Kalinin (Geneve)
Based on the paper "Tropical geometry to analyse demand"
Elizabeth Baldwin and Paul Klemperery, I will explain the notions "demand", "indivisible goods", "substitute", and "competitive equilibrium", and how they are related with the tropical Bezout theorem.
Mercredi 18 decembre 2013, 15h45, Villa Battelle
Grigory Mikhalkin (Geneve)
Lundi 16 decembre 2013, 14h30, Villa Battelle
Mikhail Shkolnikov (Geneve)
Lundi 2 decembre 2013, 14h30, Villa Battelle
Sergei Lanzat (Geneve)
Consider the standard symplectic $(\RR^{2n}, \omega_0)$, a point $p\in\RR^{2n}$
and an immersed closed orientable hypersurface $\Sigma\subset\RR^{2n}\minus{p}$,
all in general position. We study the following passage/tangency question: how many lines
in $\RR^{2n}$ pass through $p$ and tangent to $\Sigma$ parallel to the 1-dimensional
characteristic distribution $\ker\left(\omega_0\big|_{T\Sigma}\right)\subset T\Sigma$ of $\omega_0$.
We count each such line with a certain sign, and present an explicit formula for their algebraic number.
This number is invariant under regular homotopies in the class of a general position of the pair $(p, \Sigma)$,
but jumps (in a well-controlled way) when during a homotopy we pass a certain singular discriminant.
It provides a low bound to the actual number of these isotropic lines.
Lundi 18 novembre 2013, 15h00, Villa Battelle
Remi Cretois (Geneve)
This is report on a recent work of Kharlamov and Rasdeaconu.
Mercredi 13 novembre 2013, 8h45, Villa Battelle
Johannes Josi (Geneve)
Vendredi 1 novembre 2013, 15h30, Villa Battelle
Ivan Bazhov (Geneve)
Vendredi 1 novembre 2013, 14h30, Villa Battelle
Grigory Mikhalkin (Geneve)
Mercredi 30 octobre 2013, 8h45, Villa Battelle
Grigory Mikhalkin (Geneve)
Mercredi 16 octobre 2013, 8h45, Villa Battelle
Dmitry Zakharov (New York University)
The Krichever correspondence, developed by Igor Krichever in the 1970s, associates to the data of a smooth algebraic curve, a line bundle on it, and additional local information at marked points an infinite hierarchy of commuting linear differential or difference operators. These commuting operators then define solutions of non-linear integrable equations, such as the KdV, the KP, and the Toda lattice equations. My goal is to develop an analogue of this correspondence for tropical curves. The resulting equations should correspond to ultradiscrete limits of classical soliton equations. Some work in this direction has been done by specialists in integrable systems, by considering ultradiscrete limits of soliton equations, but Krichever's work suggests that the direct approach of constructing equations from algebro-geometric data is the most natural one.
Mardi 8 octobre 2013, 10h00, Villa Battelle
Nikita Kalinin (Genève)
Mercredi 2 octobre 2013, 8h45, Villa Battelle
Grigory Mikhalkin (Genève)
I'll report on some research directions that appeared in
the "Tropical geometry and topology" program in the
Max-Planck-Institute, Bonn.
Mercredi 22 mai 2013, 14h30, Villa Battelle
Maksim Karev (Genève)
The first part will be dedicated to the retelling the paper of Lizhen Ji "Complete invariant geodesic metrics on outer spaces and Jacobian varieties of tropical curves".
The second part is a progress report on my study of intersection theory in matroidal fans.
Jeudi 16 mai 2013, 16h30, Villa Battelle
Lionel Lang (Genève)
For this continuation, we will review the paper of Nilsson, Passare "Discriminant coamoebas in dimension two".
Jeudi 2 mai 2013, 16h30, Villa Battelle
Johan Björklund (Genève)
We will discuss how to construct a symplectic isotopy of smoothly isotopic symplectic curves starting from a cobordism in a symplectic manifold of dimension at least 6. We will also discuss some applications of this construction to real symplectic knots and links in P^3.
Mercredi 24 avril 2013, 14h30 à 16h00, Villa Battelle
Grigory Mikhalkin (Genève)
The talk will review the concept of harmonic amoebas (for
punctured Riemann surfaces) that generalizes amoebas of planar
algebraic curves as well as a related concept of harmonic mushrooms.
Both concepts were recently suggested by Igor Krichever.
mardi 23 avril 2013, 17h30 à 18h30, Villa Battelle
Lionel Lang (Genève)
This talk aims to be an overview on the main results obtained on coamoebas during the last decade.
Mercredi 17 avril 2013, 14h30 à 16h00, Villa Battelle
Nikita Kalinin (Genève)
I will retell the article "Tropical curves with a singularity in a fixed point" of Markwigs and Shustin.
Mercredi 13 mars 2013, 15h30 à 17h00, Villa Battelle
Max Karev (Genève)
Psi-classes are certain cohomology classes on moduli spaces of marked
curves. In a sense, Psi-classes are the the most natural classes to
consider, as they obtain nice geometrical properties and rich
combinatorics.
In my talk I am going to review G. Mikhalkin's construction of
Psi-classes on moduli spaces of tropical rational marked curves, and
propose a definition of Psi-classes on tropical M_{1;1} and M_{1;2}.
Mercredi 6 mars 2013, 14h30 à 16h00, Villa Battelle
Nikita Kalinin (Genève)
I will define multiplicity of a tropical curve at a point (via
modification or stable intersection) and prove an estimation for the minimal
degree of a curve passing through given set of points with prescribed
multiplicities.
This estimation is worse than the conjectured one, approximately in 1,4
times but possibly can lead to a construction of a counter-example.
Vendredi 22 févier 2013, 14h30 à 16h00, Villa Battelle
Mikhail Shkolnikov (Genève)
A term "categorification" first appeared in a paper by L.
Crane and I. Frenkel on algebraic structures in TQFT almost twenty
years ago. During the last decade this topic undergone rapid
development and gained a lot of attention. In very broad terms to
categorify something means to introduce another object of a categorial
sort somehow related to the first one. I will talk about abelian
categorification, which in contrast to a general concept has precise
mathematical meaning. We will discuss diagrammatic approach to the
problem and an example of Heisenberg algebra which, among all
currently known examples, looks the most visible. The talk will be
based on a mini-course given by A. Licata in Les Diablerets and papers
of M. Khovanov, A. Lauda and V. Mazorchuk.
Mardi 29 janvier 2013, 14h30 à 16h00, Villa Battelle
Lionel Lang (Genève)
We introduce the basic notions about Teichmüller spaces needed for Grisha's talk on Friday. We will focus on the Teichmüller space T(g,n) of compact Riemann surfaces of genus g with n punctures. From the formal to the conformal point of view, we aim to describe T(g,n) with the help of the so called Fenchel-Nielsen coordinates, relying on a chosen decomposition of our surfaces into hyperbolic pairs of pants.
Vendredi 1er février 2013, 14h30 à 16h00, Villa Battelle
Grigory Mikhalkin (Genève)
We formulate and sketch the proof of a series of theorems
establishing a correspondence between tropical and classical
objects.
Hyperbolic amoebas and CMC surfaces.
Séminaires passés
A presentation of the isometry
group of the Euclidean plane and the orthogonal groups O(n) using
generators and relations, following O. Viro's recent preprint
http://arxiv.org/abs/1405.1460.
Tropical geometry through lens of economic.
Some enumerative problem.
Geometry of Hilbert schemes of points on a surface.
Counting isotropic tangent lines of hypersurfaces.
Counting real curves on real K3 surfaces.
Equivariant Cohomology
Moduli spaces of linkages
Tropical Homology (continuation)
Tropical Homology
The tropical Krichever correspondence.
Yau-Zaslov approach in counting nodal curves on K3.
Questions from the tropical Summer program in Bonn.
Outer spaces and matroidal fans.
A survey on coamoebas (continuation)
Symplectic Isotopy of Symplectic Curves in Higher Dimensions.
On amoebas and mushrooms (after I. Krichever)
A survey on coamoebas
Tropical singularities via Bergman fans
Tropical Psi-classes on M_{0;n}, M_{1;1} and M_{1,2}
Tropical version of the Nagata conjecture.
Diagrammatic abelian categorification.
A introduction to Teichmüller spaces.
Correspondence theorems in tropical geometry.