1 dimensional DLA: transient walks
We explore the diameter growth of 1-dimensional long range DLA. I will describe some older results, and then focus on new results for transient walks. With Amir and Kozma.
Chargement de la vue.
Approximate cloaking using transformation optics and negative index materials
ENS Salle WIn this talk, I will discuss some results and analysis on the approximate cloaking using transformation optics and negative index materials.
La mesure harmonique des arbres de Galton-Watson
Salle à confirmerPositivity of line bundles on varieties defined over non-Archimedean fields
IHP Salle 314For algebraic varieties defined over the complex numbers, one can study geometry using both algebraic and analytic methods. Over a non-Archimedean field, one can try to do the same thing using Berkovich spaces. I will discuss positivity notions for metrics on line bundles on varieties defined over discretely or trivially valued fields.
NIP, amenability, and dynamics
IHP Salle 314I will discuss problems around definably amenable groups in NIP theories, informed by some invariants coming from topological dynamics.
Newton-Puiseux Theorem for convergent generalised power series
IHP Salle 314A generalised power series (in several variables) is a series with real nonnegative exponents whose support is contained in a cartesian product of well-ordered subsets of the real line. Let A be the collection of all convergent generalised power series. I will show that, if f(x_1,...,x_n,y) is in A, then the solutions y=g(x_1,...,x_n) of the equation f=0 can be expressed as terms of the language which has a symbol for every function in A and a symbol for division. The construction of the terms is rather explicit. If instead of […]
Noncommutative Laurent phenomenon
IHP Salle 314A composition of birational maps given by Laurent polynomials need not be a Laurent polynomial. When it does, we talk about the Laurent phenomenon. A large variety of examples of the Laurent phenomenon for commuting variables comes from the theory of cluster algebras introduced by Fomin and Zelevinsky. Much less is know in the noncommutative case. I will discuss various noncommutative Laurent phenomena including examples coming from noncommutative triangulations of polygons and oriented surfaces. As a byproduct of the theory, I will outline a proof of Laurentness of a noncommutative […]
Noncommutative birational transformations
IHP Salle 314I will present several examples of group actions by birational transformations in free noncommuting variables. One of examples is related to the talk of V.Retakh on noncommutative Laurent phenomenon, while another (a noncommutative generalization of the Coble action of Coxeter groups of series E) is definitely not cluster.
DAHA and Torus Knots
IHP Salle 314The talk will be an introduction to the new theory of the refined Jones and Quantum Group invariants of torus knots based on double affine Hecke algebras. This approach provides formulas (though mainly conjectural) for Poincare polynomials of stable Khovanov-Rozansky homology, also called super-polynomials, related to the BPS states from String theory. Khovanov-Rozansky theory will be touched upon only a little