14.00-14.45 Julien Cassaigne (IML, Marseille): A family of infinite words with complexity 2n+1 associated with a bidimensional continued fraction algorithm15.00-15.45 Milton Minervino (LaBRI, Bordeaux): Fractals de Rauzy et substitutions d'arbre15.45-16.15 coffee break16.45-17.00 Nathalie Aubrun (ENS, Lyon): Tilings problems on substitution orbits
Let f be a morphism of projective smooth varieties X, Y defined over the rationals. The conjecture by Colliot-Thélène under discussion gives (conjectural) sufficient conditions which imply that for almost all rational prime numbers p, the map f maps the p-adic points X(Q_p) surjectively onto Y(Q_p). The aim of the talk is to present some recent results by Denef, Skorobogatov et al
The dynamical Mordell-Lang conjecture in characteristic zero predicts that if f : X --> X is a map of algebraic varieties over a field K of characteristic zero, Y subset X is a closed subvariety and a in X(K) is a K-rational point on X, then the return set { n in N : f^n(a) in Y(K) } is a finite union of points and arithmetic progressions. For K a field of characteristic p > 0, it is necessary to allow for finite unions with sets of the form { […]
(Joint work with A. Chernikov)Let V subseteq C^3 be a complex variety of dimension 2.The Elekes-Szabo Theorem says that if V contains `too many' points on n x n x n Cartesian products then V has a special form: either V contains a cylinder over a curve or V is related to the graph of the multiplication of an algebraic group.In this talk we generalize the Elekes-Szabo Theorem to relations on strongly minimal sets interpretable in distal structures.
14.00-14.45 Omer Tamuz (Caltech): The Poisson boundary and the infinite conjugacy class property15.00-15.45 Yair Hartman (Northwestern University): Stationary C*-Dynamical Systems15.45-16.15 pause café16.15-17.00 Said Sidki (University of Brasilia): Self-similarity and finite presentability
On décrit le groupe de Griffiths du produit d'une courbe C et d'une surface S comme un quotient du noyau d'Albanese de S pris sur le corps des fonctions de C. Quand C est une section hyperplane de S variant dans un pinceau de Lefschetz, une modification convenable du graphe du plongement de C dans S a une classe dans Griff(CxS). On démontre que cette classe est non nulle pour une infinité de membres du pinceau lorsque le corps de base k est de caractéristique 0, que le genre géométrique […]
For a prime number p and a non-negative integer n we consider a Morava K-theory K(n) with the coefficient ring ?p. This is a universal oriented cohomology theory in the sense of Levine-Morel with a pn-typical formal group law which has height n modulo p. It turns out that K(n) is strongly related to cohomological invariants of algebraic groups in the sense of Serre. This is our starting point to compute the Chow groups of quadrics from the powers Im+2 of the fundamental ideal of the Witt ring up to […]
14.00-14.45 Thomas Schick (Göttingen): Approximation of L2-Betti numbers and the algebraic Eigenvalue property (after Jaikin-Zaipirain)15.00-15.45 Jacques Darné (Lille): Variations autour du problème d'Andreadakis 15.45-16.15 pause café16.15-17.00 Volodymyr Nekrashevych (Texas A&M): Amenability of iterated monodromy groups
To every group G is associated an associative algebra, namely its group ring kG. Which (geometric) properties are reflected in (algebraic) properties of kG? I will survey some results and conjectures in this area, concentrating on specific examples: growth, amenability, torsion, and filtrations.
About fifteen years ago, Thomas Scanlon and I gave a description of sets that arise as the intersection of a subvariety with a finitely generated subgroup inside a semiabelian variety over a finite field. Inspired by later work of Derksen on the positive characteristic Skolem-Mahler-Lech theorem, which turns out to be a special case, Jason Bell and I have recently recast those results in terms of finite automata. I will report on this work, as well as on the work-in-progress it has engendered on an effective version of the isotrivial […]
A doubling chart on an n-dimensional complex manifold Y is a univalent analytic mapping psi : B_1
(Travail en commun avec E. Hrushovski)Le but de cet exposé sera de montrer qu'il n'y a que deux corps interprétables (à isomorphisme définissable près) dans ACVF. On commencera par rappeler des résultats de classification des groupes (abéliens) interprétables dans ACVF puis on appliquera ces résultats à l'étude des corps.
