Informations pratiques
Dates : du 15 juin au 17 juin.Rendez-vous au LAREMA lundi à 11h en salle café.
Dîner de conférence le mardi 16 juin à 19h à la Réserve.
Déjeuners au FJT Darwin.
Lundi après-midi : salle I001.
Mardi matin : salle I006.
Mardi après-midi : salle I006.
Mercredi matin : salle I006.
Emploi du temps prévisionnel
| Lundi (i001) | Mardi (i006) | Mercredi (i006) | |
| 9h15 - 10h15 | Arrivées. | Théo Jaudon | Ronan Quarez |
| 10h45 - 11h45 | Antonio Carbone | Nicolas Dutertre | |
| 12h00 - 13h00 | Déjeuner au FJT Darwin | Déjeuner au FJT Darwin | Déjeuner au FJT Darwin |
| 14h00 - 15h00 | Jimmy Guillou | Enrico Savi | Discussions libres. |
| 15h30 - 16h30 | Aurore Boitrel | Antoine Boivin | |
| Dîner à La Réserve à 19h |
Résumés
Aurore Boitrel - Automorphism groups of real rational Del Pezzo surfaces of degree 4.
Del Pezzo surfaces and their automorphism groups play a key role in the classification up to conjugacy of finite subgroups of the Cremona group of the plane.Over an algebraically closed field, they are completely classified together with their automorphism groups.
In this talk, we will focus on real rational Del Pezzo surfaces of degree 4. Unlike larger degrees, the degree 4 case involves an infinite moduli space of surfaces, already over the complex numbers.
We will explain how studying the actions of automorphisms and of the Galois group on the conic bundle structures enables us to give a complete description of their automorphism groups by generators in terms of automorphisms and birational automorphisms.
Antoine Boivin - Seminormal toric varieties.
Toric varieties are usually assumed to be normal in order to obtain a complete combinatorial description via fans of cones in ℝⁿ.This provides a dictionary between the geometric properties of these toric varieties and the combinatorial properties of the fans.
Pedro Daniel González Pérez and Bernard Teissier have extended this equivalence to non-normal toric varieties by considering fans with the additional data of a family of compatible monoids.
In a joint work with François Bernard, we study an intermediate class of toric varieties, called “semi-normal”, and prove, using a result by Les Reid and Leslie Roberts on the semi-normalization of monoids, that they are equivalent to the data of a combinatorial object we have called “fans with attached groups”.
We thus obtain a class of toric varieties with singularities that are more general than those of normal varieties, while having a combinatorial structure which is much simpler than that of general non-normal toric varieties.
Antonio Carbone - Desingularization of closed semialgebraic sets and applications.
Abstract available here.Nicolas Dutertre - Lê-Greuel type formulas for some mappings from (ℝⁿ,0) to (ℝ²,0).
We consider a definable map-germ (f,g) :(ℝⁿ,0) → (ℝ²,0). Under some conditions on f and g, we establish Lê-Greuel type formulas, namely we relate the following quantities:χ ({f=α} ∩ {g=δ} ∩ Bεⁿ),
χ ({f=α} ∩ {g≥δ} ∩ Bεⁿ) − χ ({f=α} ∩ {g≤δ} ∩ Bεⁿ),
where (α,δ) is a regular value of (f,g) and 0 < |(α,δ)| ≪ ε ≪ 1, to Poincaré-Hopf indices of appropriate vector fields.
Our method is based on Lagrange multipliers and some polar techniques.
We provide a large class of weighted-homogeneous mappings for which our conditions are satisfied.
Joint work with Juan Antonio Moya Pérez (University of Valencia).
Jimmy Guillou - Applications analytiques par arcs équivariantes de ℝ²→ℝ² avec ℤ/2ℤ qui agit sur ℝ² par changement de signe des coordonnées.
Théo Jaudon - Poles of real motivic zeta functions for curves.
To a real polynomial function germ f : (ℝᵈ,0) → (ℝ,0), one can associate a real motivic zeta function Zmot,0(f;𝕃⁻ˢ), as well as motivic zeta functions with signs Zmot,0±(f;𝕃⁻ˢ).These functions are invariants (with respect to the blow-Nash equivalence) of the singularities of the real locus of f in a neighborhood of the origin and they can be expressed in terms of an embedded resolution of f.
By adapting Veys' work to the real setting, we provide a description of the poles of these functions in the case where f ∈ ℝ[x,y].
Ronan Quarez - Une version réelle de la notion d'extension de corps purement inséparable ?
Enrico Savi - On the first-order theory of quaternions
In complex and real algebraic geometry, the question on how projections of algebraic sets behave is completely understood by the celebrated Chevalley's theorem and Tarski-Seidenberg principle, respectively.In general, the latter geometric problem has a very clear interpretation in model theory, which in turn is also very useful for geometric applications.
The aim of this talk is to investigate the quaternionic version of the latter problem by completely characterizing the models of the first-order theory of quaternions and proving some fundamental properties, such as completeness and model completeness.
Then, we will focus on consequences in algebraic geometry over ℍ by introducing a good notion for the Zariski topology of ℍⁿ and by describing first properties of algebraic subsets of ℍⁿ.
