### On centauric subshifts

Andrei Romashchenko
We discuss subshifts of finite type (tilings) that combine virtually opposite properties, being at once very simple and very complex. On the one hand, the combinatorial structure of these subshifts is rather simple: we require that all their configurations are quasiperiodic, or even that all configurations contain exactly the same finite patterns (in the last case a subshift is transitive, i.e., irreducible as a dynamical system). On the other hand, these subshifts are complex in...

### High-order Magnus integrators for non-autonomous linear evolution equations

Mechthild Thalhammer
The class of commutator-free Magnus integrators is known to provide a favourable alternative to standard interpolatory Magnus integrators, in particular for large-scale applications arising in the time integration of non-autonomous linear evolution equations. A high-order commutator-free Magnus integrator is given by a composition of several exponentials that comprise certain linear combinations of the values of the defining operator at specified nodes. Due to the fact that previously proposed commutator-free Magnus integrators of order five or...

### 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...

### Inverse problems in econometrics: examples and specific theoretical problems. Lecture 4

Jean-Pierre Florens

### Copulas based inference for discrete or mixed data

Bruno Rémillard
In this talk I will introduce the multilinear empirical copula for discrete or mixed data and its asymptotic behavior will be studied. This result will then be used to construct inference procedures for multivariate data. Applications for testing independence will be presented.

### Approximate Bayesian Computation methods for model choice a machine learning point of view - Part 1

Jean-Michel Marin
Approximate Bayesian computation (ABC) techniques, also known as likelihood-free methods, have become a standard tool for the analysis of complex models, primarily in population genetics. The development of new ABC methodologies is undergoing a rapid increase in the past years, as shown by multiple publications, conferences and softwares. In this lecture, we introduce some recent advances on ABC techniques, notably for model choice problems.

### Big Data: Tremendous challenges, great solutions

Luc Bougé
L'apparition des "Big Data" est en train de modifier profondément notre compréhension du traitement algorithmique de l'information. Le centre de gravité s'est déplacé du calcul vers les données, et le passage à l'échelle est devenu une notion centrale. En particulier, la prise en compte de la localisation géographique des données, du coût de leur déplacement et de leur disponibilité sont devenus des facteurs majeurs de la conception des applications. Cette nouvelle vision "centrée sur les...

### Interview au CIRM : Jean-Pierre Serre avec Jean-Louis Colliot-Thélène

Jean-Louis Colliot-Thélène & Jean-Pierre Serre
Jean-Pierre Serre est un mathématicien français, plus jeune Médaille Fields en 1954, il fut également le premier lauréat du Prix Abel en 2003. Jean-Louis Colliot-Thélène est un mathématicien français, Directeur de recherches à l'Université Paris-Sud, il étudie principalement la théorie des nombres et la géométrie algébrique.

### An Obata-Lichnerowicz theorem for stratified spaces

Ilaria Mondello
In the first part of this talk we will show how classical tools of Riemannian geometry can be used in the setting of stratfied spaces in order to obtain a lower bound for the spectrum of the Laplacian, under an appropriate assumption of positive curvature. Such assumption involves the Ricci tensor on the regular set and the angle along the stratum of codimension 2. We then show that a rigidity result holds when the lower...

### Multiscale model reduction for flows in heterogeneous porous media

Victor Calo
We combine discrete empirical interpolation techniques, global mode decomposition methods, and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM), to reduce the computational complexity associated with nonlinear flows in highly-heterogeneous porous media. To solve the nonlinear governing equations, we employ the GMsFEM to represent the solution on a coarse grid with multiscale basis functions and apply proper orthogonal decomposition on a coarse grid. Computing the GMsFEM solution involves calculating the residual...

### Interview at CIRM: Marc Peigné

Marc Peigné
Marc Peigné is the President of the French Mathematical Society (SMF) since June 2013. The French Mathematical Society, Société Mathématique de France, was founded in 1872 although moves towards the creation of the Society began two years earlier. It was created for defending and promoting mathematics and mathematicians. From the year after the Society was founded the Society has published the Bulletin de Société Mathématique de France which intends to be one of the greatest...

### Differential forms and the Hölder equivalence problem - Part 1

Pierre Pansu
A sub-Riemannian distance is obtained when minimizing lengths of paths which are tangent to a distribution of planes. Such distances differ substantially from Riemannian distances, even in the simplest example, the 3-dimensional Heisenberg group. This raises many questions in metric geometry: embeddability in Banach spaces, bi-Lipschitz or bi-Hölder comparison of various examples. Emphasis will be put on Gromov's results on the Hölder homeomorphism problem, and on a quasisymmetric version of it motivated by Riemannian geometry.

### Commutative algebra for Artin approximation - Part 1

Herwig Hauser
In this series of four lectures we develop the necessary background from commutative algebra to study solution sets of algebraic equations in power series rings. A good comprehension of the geometry of such sets should then yield in particular a "geometric" proof of the Artin approximation theorem. In the first lecture, we review various power series rings (formal, convergent, algebraic), their topology ($m$-adic, resp. inductive limit of Banach spaces), and give a conceptual proof of...

### Interview at CIRM: Igor Shparlinski

Igor Shparlinski
Igor Shparlinski held the Jean Morlet Chair from February 2014 to August 2014. This chair was linked in parts to the thematic month on 'Arithmetics' which took part in February 2014 at CIRM. Igor Shparlinski has a career in Number theory and its applications to cryptography, with significant overlap with the research interests of the groups Dynamique Arithmétique, Combinatoire (DAC) and Arithmétique et Théorie de l'Information (ATI) in Marseille. The idea was to start the...

### Random walk on random digraph

Justin Salez
A finite ergodic Markov chain exhibits cutoff if its distance to equilibrium remains close to its initial value over a certain number of iterations and then abruptly drops to near 0 on a much shorter time scale. Originally discovered in the context of card shuffling (Aldous-Diaconis, 1986), this remarkable phenomenon is now rigorously established for many reversible chains. Here we consider the non-reversible case of random walks on sparse directed graphs, for which even the...

### A hitchhiker's guide to Khovanov homology - Part I

Paul Turner
There are already too many introductory articles on Khovanov homology and certainly another is not needed. On the other hand by now - 15 years after the invention of subject - it is quite easy to get lost after having taken those first few steps. What could be useful is a rough guide to some of the developments over that time and the summer school Quantum Topology at the CIRM in Luminy has provided the...

### A test for local white noise (and the absence of aliasing) in locally stationary wavelet time series

Guy Nason
This talk develops a new test for local white noise which also doubles as a test for the lack of aliasing in a locally stationary wavelet process. We compare and contrast our new test with the aliasing test for stationary time series due to Hinich and co-authors. We show that the test is robust to mismatch of analysis and synthesis wavelet. We demonstrate the effectiveness of the test on some simulated examples and on an...

Paul Gauduchon

### Numerical studies of space filling designs: optimization algorithm and subprojection properties

Bertrand Iooss
discrepancy, optimal design, Latin Hypercube Sampling, computer experiment

### Formal verification of numerical analysis programs

Sylvie Boldo
From a (partial) differential equation to an actual program is a long road. This talk will present the formal verification of all the steps of this journey. This includes the mathematical error due to the numerical scheme (method error), that is usually bounded by pen-and-paper proofs. This also includes round-off errors due to the floating-point computations. The running example will be a C program that implements a numerical scheme for the resolution of the one-dimensional...

### Nonconventional limit theorems in probability and dynamical systems

Yuri Kifer
We discuss various limit theorems for "nonconventional" sums of the form $\sum ^N_{n=1}F\left ( \xi \left ( n \right ),\xi \left ( 2n \right ),...,\xi \left ( \ell n \right ) \right )$ where $\xi \left ( n \right )$ is a stochastic process or a dynamical system. The motivation for this study comes, in particular, from many papers about nonconventional ergodic theorems appeared in the last 30 years. Such limit theorems describe multiple recurrence...

### Pourquoi l'eau tombe t-elle d'un verre qu'on retourne?

Olivier Soulard
The purpose of this presentation is to describe the basic phenomenology of the Rayleigh-Taylor instability, from its early linear phase to its late turbulent and self-similar regime. Simple experiments are performed to illustrate this phenomenology. fluid mechanics - Rayleigh-Taylor instability - turbulence

### 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...

### Lagrange and water waves

Jean-Claude Saut
Lagrange - 19th century - water waves

### Robust sequential learning with applications to the forecasting of electricity consumption and of exchange rates

Gilles Stoltz
Sometimes, you feel you’re spoilt for choice: there are so many good predictors that you could use! Why select and focus on just one? I will review the framework of robust online aggregation (also known as prediction of individual sequences or online aggregation of expert advice). This setting explains how to combine base forecasts provided by ensemble methods. No stochastic modeling is needed and the performance achieved is comparable to the one of the best...

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