### Equipe Analyse Algébrique

Responsable d’équipe : François Loeser
Responsables adjoints : Penka GEORGIEVA, Maxime ZAVIDOVIQUE
Gestionnaire : Julienne PASSAVE

### Journée de rentrée, le 21/10/2021

Programme de la journée de rentrée de l’équipe AA, le 21/10/2021

En salle 15.16.413

15h-17h20 : Exposés des post-doctorants de l’équipe (titres et résumés plus bas)

15h-15h40 : Dusan Joksimovic

15h50-16h30 : Bernhard Reinke

16h40-17h20 : Jinhe Ye

17h30-18h : Réunion de l’équipe

À partir de 18h15 : pot sous la barre 24-25 niveau Jussieu

Résumés des exposés :

Dusan Joksimovic
Title : No symplectic-Lipschitz structures on $S^{2n \geq 4}$

Abstract: One of the central questions in $C^0$-symplectic geometry is whether spheres (of dimension at least 4) admit symplectic topological atlas (i.e. atlas whose transition functions are symplectic homeomorphisms). In this talk, we will prove that the answer is « no » if we replace the word « topological » with « Lipschitz ». More precisely, we will prove that every closed symplectic-Lipschitz manifold has non-vanishing even degree cohomology groups with real coefficients. The proof is based on the fact that one can define analogs of differential forms and de Rham complex on Lipschitz manifolds which share similar properties as in the smooth setting.

Bernhard Reinke
Title : Connections between complex dynamics and algebra

Abstract: Complex dynamics and algebra are deeply connected. I will present two examples of their connection: the dynamics of root-finding methods, and iterated monodromy groups of transcendental maps.

Finding roots of a polynomial is a fundamental numerical problem. Many root-finding methods, such as the Newton’s method or the Weierstrass/Durand-Kerner method can be understood as complex dynamical systems. I will sketch how computer algebraic tools were used to show that the Weierstrass method is not generally convergent.

Iterated monodromy groups are self-similar groups associated to partial self-coverings. I will give an overview of iterated monodromy groups of post-singularly finite entire transcendental functions. These groups act self-similarly on a regular rooted tree, but in contrast to IMGs of rational functions, every vertex of the tree has countably infinite degree.

I will discuss the similarities and differences of IMGs of entire transcendental functions and of polynomials, in particular in the direction of amenability.

Jinhe Ye

Title : Curve-excluding fields

Abstract : Consider the class of fields with Char(K)=0 and x^4+y^4=1 has only 4 solutions in K, we show that this class has a model companion, which we denote by CXF, curve-excluding fields. Curve-excluding fields provides examples to various questions. Model theoretically, they are model complete and algebraically bounded. Field theoretically, they are not large. This answers a question of Junker and Macintyre negatively. Joint work with Will Johnson and Erik Walsberg.

### Journée de fin d’année, jeudi 1er juillet

Amphi 24

14h-16h : Exposés courts des doctorants de l’équipe (titres plus bas)

16h-17h : réunion de fin d’année de l’équipe

À partir de 17h : pot dans le patio de l’amphi 24

14h-14h15 Antoine Toussaint

Orientations complexes des surfaces algébriques réelles

14h15-14h30 Flavien Grycan-Gérard

Entropie polynomiale des systèmes intégrables hamiltoniens à singularités modérées

14h30-14h45 Perla Azzi

Distance aux strates d’isotropie appliquée à l’espace des tenseurs d’élasticité

14h45-15h Thibaut Mazuir

Algèbre supérieure de la théorie de Morse

15h-15h15 Mahya Mehrabdollahei

Les mesures de Mahler d’une famille de polynômes exacts

15h15-15h30 An Khuong Doan

Equivariant (derived) deformations of algebraic schemes and of complex compact manifolds

15h30-15h45 Benoît Joly

Codes barres d’homéomorphismes hamiltoniens de surfaces