948 Works

Algebraic sums and products of univoque bases

Karma Dajani
Given $x\in(0, 1]$, let ${\mathcal U}(x)$ be the set of bases $\beta\in(1,2]$ for which there exists a unique sequence $(d_i)$ of zeros and ones such that $x=\sum_{i=1}^{\infty}{{d_i}/{\beta^i}}$. In 2014, Lü, Tan and Wu proved that ${\mathcal U}(x)$ is a Lebesgue null set of full Hausdorff dimension. In this talk, we will show that the algebraic sum ${\mathcal U}(x)+\lambda {\mathcal U}(x)$, and the product ${\mathcal U}(x)\cdot {\mathcal U}(x)^{\lambda}$ contain an interval for all $x\in (0, 1]$...

Statistical inverse problems and geometric "wavelet" construction

Gérard Kerkyacharian
In the fist part of the talk, we will look to some statistical inverse problems for which the natural framework is no more an Euclidian one. In the second part we will try to give the initial construction of (not orthogonal) wavelets -of the 80 - by Frazier, Jawerth,Weiss, before the Yves Meyer ORTHOGONAL wavelets theory. In the third part we will propose a construction of a geometric wavelet theory. In the Euclidian case, Fourier...

Optimal rates for $k$-NN density and mode estimation

Samory Kpotufe
We present two related contributions of independent interest: high-probability finite sample rates for $k$-NN density estimation, and practical mode estimators – based on $k$-NN – which attain minimax-optimal rates under surprisingly general distributional conditions. $k$-nearest neighbor ($k$-NN) - $k$-NN density rates - mode estimation

$k$-sum free sets in $[0,1]$

Anne De Roton
Let $k > 2$ be a real number. We inquire into the following question : what is the maximal size (inner Lebesque measure) and the form of a set avoiding solutions to the linear equation $x + y = kz$ ? This problem was used for $k$ an integer larger than 4 to guess the density and the form of a corresponding maximal set of positive integers less than $N$. Nevertheless, in the case $k...

On the space highway to Lagrange points!

Emmanuel Trélat
Everything is under control: mathematics optimize everyday life. In an empirical way we are able to do many things with more or less efficiency or success. When one wants to achieve a parallel parking, consequences may sometimes be ridiculous... But when one wants to launch a rocket or plan interplanetary missions, better is to be sure of what we do. Control theory is a branch of mathematics that allows to control, optimize and guide systems...

Moments of a Thue-Morse generating function

Hugh L. Montgomery
Let $s(m)$ denote the number of distinct powers of 2 in the binary representation of $m$. Thus the Thue-Morse sequence is $(-1)^{s(m)}$ and $T_n(x)=\sum_{0\leq m< 2^n}(-1)^{s(m)}e(mx)=\prod_{0\leq r< n}(1-e(2^rx))$ is a trigonometric generating generating function of the sequence. The work of Mauduit and Rivat on $(-1)^{s(p)}$ depends on nontrivial bounds for $\left \| T_n \right \|_1$ and for $\left \| T_n \right \|_\infty $. We consider other norms of the $T_n$. For positive integers $k$ let...

Cancellations in random nodal sets

Giovanni Peccati
I will discuss second order results for the length of nodal sets and the number of phase singularities associated with Gaussian random Laplace eigenfunctions, both on compact manifolds (the flat torus) and on subset of the plane. I will mainly focus on 'cancellation phenomena' for nodal variances in the high-frequency limit, with specific emphasis on central and non-central second order results. Based on joint works with F. Dalmao, D. Marinucci, I. Nourdin, M. Rossi and...

On the Hodge-Kodaira Laplacian on the canonical bundle of a compact Hermitian complex space

Francesco Bei
Hermitian complex spaces are a large class of singular spaces that include for instance projective varieties endowed with the metric induced by the Fubini-Study metric. Many of the problems raised by Cheeger, Goresky and MacPherson in the case of complex projective varieties admit a natural extension also in this setting. The aim of this talk is to report about some recent results concerning the Hodge-Kodaira Laplacian acting on the canonical bundle of a compact Hermitian...

Amenable groups - Lecture 2

Laurent Bartholdi
I shall discuss old and new results on amenability of groups, and more generally G-sets. This notion traces back to von Neumann in his study of the Hausdorff-Banach-Tarski paradox, and grew into one of the fundamental properties a group may / may not have -- each time with important consequences. Lecture 1. I will present the classical notions and equivalent definitions of amenability, with emphasis on group actions and on combinatorial aspects: Means, Folner sets,...

Unique ergodicity of geodesic flow in an infinite translation surface

Kasra Rafi
The behaviour of infinite translation surfaces is, in many regards, very different from the finite case. For example, the geodesic flow is often not recurrent or is not even defined for infinite time in a generic direction. However, we show that if one focuses on a class of infinite translation surfaces that exclude the obvious counter-examples, one can adapted the proof of Kerckhoff, Masur, and Smillie and show that the geodesic flow is uniquely ergodic...

Lecture on Delone sets and tilings

Boris Solomyak
In this lecture we focus on selected topics around the themes: Delone sets as models for quasicrystals, inflation symmetries and expansion constants, substitution Delone sets and tilings, and associated dynamical systems.

Criteria for equivalence between power series and polynomials

Wojciech Kucharz
Let $A$ be the ring of formal power series in $n$ variables over a field $K$ of characteristic zero. Two power series $f$ and $g$ in $A$ are said to be equivalent if there exists a $K$-automorphism of $A$ transforming $f$ into $g$. In my talk I will review criteria for a power series to be equivalent to a power series which is a polynomial in at least some of the variables. For example, each...

Interview au CIRM : Yvon Maday

Yvon Maday
Le CIRM : écrin estival du CEMRACS depuis 20 ans !

Operators in ergodic theory - Lecture 3: Compact semigroups and splitting theorems

Markus Haase
The titles of the of the individual lectures are: 1. Operators dynamics versus base space dynamics 2. Dilations and joinings 3. Compact semigroups and splitting theorems

The anisotropic Calderon problem

David Dos Santos Ferreira
The anisotropic Calderon problem is whether it is possible to determine a Riemannian metric (modulo the natural invariance by isometries) on a compact Riemannian manifold with boundary from knowledge of the Cauchy data of harmonic functions. This problem is solved in dimension two, as well as in the conformal class of the Euclidean metric and for analytic metrics, but remains challenging for smooth metrics in dimension higher than three. In this talk I will present...

Least squares regression Monte Carlo for approximating BSDES and semilinear PDES

Plamen Turkedjiev
In this lecture, we shall discuss the key steps involved in the use of least squares regression for approximating the solution to BSDEs. This includes how to obtain explicit error estimates, and how these error estimates can be used to tune the parameters of the numerical scheme based on complexity considerations. The algorithms are based on a two stage approximation process. Firstly, a suitable discrete time process is chosen to approximate the of the continuous...

Independence of normal words

Verónica Becher
Recall that normality is a elementary form of randomness: an infinite word is normal to a given alphabet if all blocks of symbols of the same length occur in the word with the same asymptotic frequency. We consider a notion of independence on pairs of infinite words formalising that two words are independent if no one helps to compress the other using one-to-one finite transducers with two inputs. As expected, the set of independent pairs...

Differential descent obstructions

José Felipe Voloch
We will discuss a new obstruction to the existence of rational and integral points on algebraic varieties over function fields obtained by considering covers described by differential equations.

Plant ecology influences population genetics: the role of seed banks in structuring genetic diversity

Aurélien Tellier
Recent population genomics studies focus prevalently on the aspects of demography and adaptation, whereas age structure (for example, in plants via the maintenance of seed banks) has attracted less attention. Germ banking, that is, seed or egg dormancy, is a prevalent and important life-history trait in plants and invertebrates, which buffers against environmental variability and modulates species extinction in fragmented habitats. I will here summarize our recent findings investigating the intertwined effect of germ banking,...

Mutually enriching connections between ergodic theory and combinatorics - part 3

Vitaly Bergelson
² The early results of Ramsey theory : Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres. ² Three main principles of Ramsey theory : First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of this result. Third principle: The sought-after configurations which are always...

Maps between curves and diophantine obstructions

José Felipe Voloch
Given two algebraic curves $X$, $Y$ over a finite field we might want to know if there is a rational map from $Y$ to $X$. This has been looked at from a number of perspectives and we will look at it from the point of view of diophantine geometry by viewing the set of maps as $X(K)$ where $K$ is the function field of $Y$. We will review some of the known obstructions to the...

Reconstruction methods for ill-posed inverse problems - Part 2

Samuli Siltanen
inverse problem - reconstruction - regularization - tomography - computation

Towards static analysis of functional programs using term rewriting and tree automata

Thomas Genet
Tree Automata Completion is an algorithm computing, or approximating, terms reachable by a term rewriting system. For many classes of term rewriting systems whose set of reachable terms is known to be regular, this algorithm is exact. Besides, the same algorithm can handle ²²any²² left-linear term rewriting system, in an approximated way, using equational 2 abstractions. Thanks to those two properties, we will see that regular languages and tree automata completion provide a promising alternative...

Registration Year

  • 2017

Resource Types

  • Audiovisual