### Inexact gradient projection and fast data driven compressed sensing: theory and application

Michael E. Davies
We consider the convergence of the iterative projected gradient (IPG) algorithm for arbitrary (typically nonconvex) sets and when both the gradient and projection oracles are only computed approximately. We consider different notions of approximation of which we show that the Progressive Fixed Precision (PFP) and (1+epsilon) optimal oracles can achieve the same accuracy as for the exact IPG algorithm. We also show that the former scheme is also able to maintain the (linear) rate of...

### Uniform distribution mod 1, results and open problems

Imre Katai
Given a fixed integer $q \geq 2$, an irrational number $\xi$ is said to be a $q$-normal number if any preassigned sequence of $k$ digits occurs in the $q$-ary expansion of $\xi$ with the expected frequency, that is $1/q^k$. In this talk, we expose new methods that allow for the construction of large families of normal numbers. This is joint work with Professor Jean-Marie De Koninck.

### Space-time covariance of KPZ growth models

Patrik Ferrari
For some growth models in the Kardar-Parisi-Zhang universality class, the large time limit process of the interface profile is well established. Correlations in space-time are much less understood. Along special space-time lines, called characteristics, there is a sort of ageing. We study the covariance of the interface process along characteristic lines for generic initial conditions. Joint work with A. Occelli (arXiv:1807.02982).

### Bayesian modelling

Kerrie Mengersen
This tutorial will be a beginner’s introduction to Bayesian statistical modelling and analysis. Simple models and computational tools will be described, followed by a discussion about implementing these approaches in practice. A range of case studies will be presented and possible solutions proposed, followed by an open discussion about other ways that these problems could be tackled.

### Fluid-structure interaction in the cardiovascular system. Lecture 2: Cardiac valves

Jean-Frédéric Gerbeau
I will introduce the topic of computational cardiac electrophysiology and electrocardiograms simulation. Then I will address some questions of general interest, like the modeling of variability and the extraction of features from biomedical signals, relevant for identification and classification. I will illustrate this research with an example of application to the pharmaceutical industry.

### Interview au CIRM : Claire Voisin

Claire Voisin
Claire Voisin, mathématicienne française, est Directrice de recherche au Centre national de la recherche scientifique (CNRS) à l'Institut de mathématiques de Jussieu, elle est membre de l'Académie des sciences et titulaire de la nouvelle chaire de mathématiques « géométrie algébrique » au Collège de France. Elle a reçu de nombreux prix nationaux et internationaux pour ses travaux en géométrie algébrique, et en particulier pour la résolution de la conjecture de Koidara sur les variétés de...

### ​​​​Mixing and the local central limit theorem for hyperbolic dynamical systems

Péter Nándori
We present a convenient joint generalization of mixing and the local version of the central limit theorem (MLLT) for probability preserving dynamical systems. We verify that MLLT holds for several examples of hyperbolic systems by reviewing old results for maps and presenting new results for flows. Then we discuss applications such as proving various mixing properties of infinite measure preserving systems. Based on joint work with Dmitry Dolgopyat.

### Equidistribution of square-tiled surfaces, meanders, and Masur-Veech volumes

Anton Zorich
We show how recent results of the authors on equidistribution of square-tiled surfaces of given combinatorial type allow to compute approximate values of Masur-Veech volumes of the strata in the moduli spaces of Abelian and quadratic differentials by Monte Carlo method. We also show how similar approach allows to count asymptotical number of meanders of fixed combinatorial type in various settings in all genera. Our formulae are particularly efficient for classical meanders in genus zero....

### Interview at Cirm: Shigeki Akiyama

Shigeki Akiyama
Chaire Jean-Morlet - 2017 semester 2: Tiling and Discrete Geometry. Shigeki Akiyama is Professor at the Institute of Mathematics of the University of Tsukuba, Japan. A regular organizer of the annual workshop on quasi-periodic tilings at RIMS, he has also spent time as organizer or invited professor on several occasions in France (Paris, Marseille, Strasbourg) but also in Debrecen and at the Chinese University of Hong-Kong.

### Preprojective algebras and Cluster categories

Osamu Iyama
The preprojective algebra $P$ of a quiver $Q$ has a family of ideals $I_w$ parametrized by elements $w$ in the Coxeter group $W$. For the factor algebra $P_w = P/I_w$, I will discuss tilting and cluster tilting theory for Cohen-Macaulay $P_w$-modules following works by Buan-I-Reiten-Scott, Amiot-Reiten-Todorov and Yuta Kimura.

### Were the foundations of measurement without theory laid in the 1920s?

In his 1947 essay, Tjalling Koopmans criticized the development of an empirical science that had no theoretical basis, what he referred to as measurement without theory. The controversy over the status of relations based on mere statistical inference has not ceased since then. Instead of looking for the contemporary consequences, however, I will inquire into its early beginnings. As early as the 1900s, Walras, Pareto and Juglar exchanged views on the status of theory and...

### ​​​Growth of normalizing sequences in limit theorems

Sébastien Gouëzel
​Assume that a renormalized Birkhoff sum $S_n f/B_n$ converges in distribution to a nontrivial limit. What can one say about the sequence $B_n$? Most natural statements in the literature involve sequences $B_n$ of the form $B_n = n^\alpha L(n)$, where $L$ is slowly varying. We will discuss the possible growth rate of $B_n$ both in the probability preserving case and the conservative case. In particular, we will describe examples where $B_n$ grows superpolynomially, or where...

### ​On the motive of the stack of vector bundles on a curve

Victoria Hoskins
Following Grothendieck’s vision that a motive of an algebraic variety should capture many of its cohomological invariants, Voevodsky introduced a triangulated category of motives which partially realises this idea. After describing some of the properties of this category, I explain how to define the motive of certain algebraic stacks. I will then focus on defining and studying the motive of the moduli stack of vector bundles on a smooth projective curve and show that this...

### From cluster algorithms to PDMP algorithms: a Monte Carlo story of symmetry exploitation

Manon Michel
During this talk, I will present how the development of non-reversible algorithms by piecewise deterministic Markov processes (PDMP) was first motivated by the impressive successes of cluster algorithms for the simulation of lattice spin systems. I will especially stress how the spin involution symmetry crucial to the cluster schemes was replaced by the exploitation of more general symmetry, in particular thanks to the factorization of the energy function.

### On the cross-combined measure of families of binary lattices and sequences

Katalin Gyarmati
The cross-combined measure (which is a natural extension of crosscorrelation measure) is introduced and important constructions of large families of binary lattices with nearly optimal cross-combined measures are presented. These results are important in the study of large families of pseudorandom binary lattices but they are also strongly related to the onedimensional case: An easy method is showed obtaining strong constructions of families of binary sequences with nearly otimal cross-correlation measures based on the previous...

### A new continuum theory for incompressible swelling materials

Pierre Degond
Emergence is a process by which coherent structures arise through interactions among elementary entities without being directly encoded in these interactions. In this course, we will address some of the key questions of emergence such as the deciphering of the hidden relation between individual behavior and emergent structures. We will start with presenting biologically relevant examples of microscopic individual-based models (IBM). Then, we will develop a systematic coarse-graining approach and derive corresponding coarse-grained models (CGM)...

### Rare event simulation for molecular dynamics

This talk is devoted to the presentation of algorithms for simulating rare events in a molecular dynamics context, e.g., the simulation of reactive paths. We will consider $\mathbb{R}^d$ as the space of configurations for a given system, where the probability of a specific configuration is given by a Gibbs measure depending on a temperature parameter. The dynamics of the system is given by an overdamped Langevin (or gradient) equation. The problem is to find how...

### Magie mathématique

Antonietta Mira
​L'intérêt pour l'intelligence artificielle (IA) s'est considérablement accru ces dernières années et l'IA a été appliquée avec succès à des problèmes de société. Le Big Data, le recueil et l’analyse des données, la statistique se penchent sur l’amélioration de la société de demain. Big Data en santé publique, dans le domaine de la justice pénale, de la sécurité aéroportuaire, des changements climatiques, de la protection des espèces en voie de disparition, etc. ​ ​C'est sur...

### Interview at CIRM: Genevieve Walsh

Genevieve Walsh
'I am a geometric topologist, and I'm interested in problems in both geometric topology and geometric group theory. I study groups acting on spaces in a variety of contexts: groups acting on hyperbolic space with quotient the complement of a knot in S3, groups acting on trees, how to make a "good" space for a group to act on, and the many ways a particular group can act on a particular space. I also like...

### Geometric quantization of toric and semitoric systems

Eva Miranda
One of the many contributions of Kostant is a rare gem which probably has not been sufficiently explored: a sheaf-theoretical model for geometric quantization associated to real polarizations. Kostant’s model works very well for polarizations given by fibrations or fibration-like objects (like integrable systems away from singularities). For toric manifolds where the real polarization is determined by the fibers of the moment map, Kostant’s model yields a representation space whose dimension is the number of...

### $H^\infty$-calculus and the heat equation with rough boundary conditions

Veraar Mark
In this talk we consider the Laplace operator with Dirichlet boundary conditions on a smooth domain. We prove that it has a bounded $H^\infty$-calculus on weighted $L^p$-spaces for power weights which fall outside the classical class of $A_p$-weights. Furthermore, we characterize the domain of the operator and derive several consequences on elliptic and parabolic regularity. In particular, we obtain a new maximal regularity result for the heat equation with very rough inhomogeneous boundary data. The...

### Sur les mesures stationnaires des VLMC

Nicolas Pouyanne
Les chaînes de Markov à mémoire de longueur variable sont des sources probabilistes pour lesquelles la production d'une lettre dépend d'un passé fini, mais dont la longueur dépend du temps est n'est pas bornée. Elles sont définies à partir d'un arbre T qui est un sous-arbre de l'arbre de tous les mots. Contrairement aux chaînes de Markov d'ordre fini standard, ces sources n'admettent pas toujours de mesure de probabilité stationnaire, ou peuvent en admettre plusieurs....

### Gamma functions, monodromy and Apéry constants

Masha Vlasenko
In 1978 Roger Apéry proved irrationality of zeta(3) approximating it by ratios of terms of two sequences of rational numbers both satisfying the same recurrence relation. His study of the growth of denominators in these sequences involved complicated explicit formulas for both via sums of binomial coefficients. Subsequently, Frits Beukers gave a more enlightening proof of their properties, in which zeta(3) can be seen as an entry in a monodromy matrix for a differential equation...

### Bayesian econometrics in the Big Data Era

Sylvia Frühwirth-Schnatter
Data mining methods based on finite mixture models are quite common in many areas of applied science, such as marketing, to segment data and to identify subgroups with specific features. Recent work shows that these methods are also useful in micro econometrics to analyze the behavior of workers in labor markets. Since these data are typically available as time series with discrete states, clustering kernels based on Markov chains with group-specific transition matrices are applied...

### Introduction to quantum optics - Lecture 3

Peter Zoller
Quantum optical systems provides one of the best physical settings to engineer quantum many-body systems of atoms and photons, which can be controlled and measured on the level of single quanta. In this course we will provide an introduction to quantum optics from the perspective of control and measurement, and in light of possible applications including quantum computing and quantum communication. The first part of the course will introduce the basic quantum optical systems and...

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