14.00-14.45 Emmanuel Militon (Nice), Groups of diffeomorphisms of a Cantor set15.00-15.45 Simon André (Rennes), Hyperbolicity is preserved under elementary equivalence15.45-16.15 coffee break(CANCELED) 16.15-17.00 Nikolay Nikolov (Oxford), On conjugacy classes in compact groups
Joint with Itay Kaplan and Pierre Simon.Distal theories are NIP theories which are ?Roewholly unstable?R. Chernikov and Simon's ?Roestrong honest definitions?R characterise distal theories as those in which every type is compressible. Adapting recent work in machine learning of Chen, Cheng, and Tang on bounds on the ?Roerecursive teaching dimension?R of a finite concept class, we find that compressibility is dense in NIP structures, i.e. any formula can be completed to a compressible type in S(A). Considering compressibility as an isolation notion (which specialises to l-isolation in stable theories), we […]
The word and conjugacy problems are central decision problems associated with finitely generated groups. In particular, there are deep results which bridge some of the main concepts of the theories of computability and computational complexity with group theoretical invariants through the word problem in groups. In this talk I will recall some of the well-known facts about the word and conjugacy problems in groups as well as discuss new results concerning the relationship between them.
I will speak about joint work with Jacob Tsimerman. Let E be an elliptic curve parameterized by a modular (or Shimura) curve. There are a number of results (..., Buium-Poonen, Kuhne) to the effect that the images of CM points are (under suitable hypotheses) linearly independent in E. We consider this issue in the setting of the Zilber-Pink conjecture and prove a result which improves previous results in some aspects
The determinant method gives upper bounds for the number of rational points of bounded height on or near algebraic varieties defined over global fields. There is a real-analytic version of the method due to Bombieri and Pila and a p-adic version due to Heath-Brown. The aim of our talk is to describe a global refinement of the p-adic method and some applications like a uniform bound for non-singular cubic curves which improves upon earlier bounds of Ellenberg-Venkatesh and Heath-Brown.
Patching was first introduced as an approach to the Inverse Galois Problem. The technique was then extended to a more algebraic setting and used to prove a local-global principle by D. Harbater, J. Hartmann and D. Krashen. I will present an adaptation of the method of patching to the setting of Berkovich analytic curves. This will then be used to prove a local-global principle for function fields of curves that generalizes that of the above mentioned authors.
Étant donné un nombre premier p, nous expliquerons tout d’abord comment construire une valeur absolue sur Q, dite p-adique, puis un complété, de la même façon que l’on construit R à partir de Q. Ce complété, le corps des nombres p-adiques, possède des propriétés arithmétiques intéressantes, mais présente de nombreuses pathologies topologiques. Nous expliquerons comment y remédier en le plongeant dans un espace plus grand, un espace de Berkovich, et exposerons quelques applications.
Orderable groups are extensively studied by logicians and group theorists. In my talk I will address aspects of left- or bi-orderable groups that are connected with computability theory. In particular, I will talk about constructions of bi-orderable computable groups that cannot be embedded into groups with computable bi-order. I will also discuss our recent work in progress with M. Steenbock about simplicity and computably left-orderability.
14.00 -14.45 Cornelia Drutu (Oxford), Fixed point properties and conformal dimension of the boundary for hyperbolic groups 15.00- 15-45 Mathieu Dussaule (Nantes), The Guivarch inequality in relatively hyperbolic groups 15.45-16.15 coffee break, 16.15-17.00 Anthony Genevois (Orsay), Cubical geometry of braided Thompson's group
Dans cet exposé, nous verrons que certaines inégalités fonctionnelles jouent un rôle crucial dans l'étude du comportement en temps grand de solutions de certaines EDP. Plus précisément, nous utiliserons des méthodes dites de dissipation d'entropie (dont le but est t'établir des versions quantitatives du mécanisme de décroissance de l'entropie) dans le cas de l'équation de Fokker-Planck. Nous étudierons ensuite le cas plus complexe de l'équation de Boltzmann (homogène en espace) et verrons que ces méthodes fournissent également des résultats sur le comportement en temps grand des solutions de l'équation. Néanmoins, […]
I will give a complete description of all groups definable in Presburger arithmetic, up to finite index subgroups. This builds on previous work on bounded groups in Presburger arithmetic by Mariana Vicaria and Alf Onshuus.
The notion of ampleness captures essential properties of projective spaces over fields. It is natural to ask whether any sufficiently ample strongly minimal set arises from an algebraically closed field. In this talk I will explain the question and present recent results on ample strongly minimal structures.
