Mirror-symmetric Jacobi matrices are 3-diagonal matrices remaining invariant with respect to reflections over main diagonal and main antidiagonal. Such matrices are important in applications connected with perfect state transfer in quantum information. We demonstrate some new properties of these matrices as well as of corresponding orthogonal polynomials. We propose also a new efficient algorithm to solve inverse spectral problem for these matrices.

# Seminar Physique Mathématique -- Mirror-symmetric Jacobi matrices and their applications

# Logic, Category Theory, and Computation -- The simplex of invariant measures of a minimal homeomorphism

We give a characterization of all simplices of probability measures on a Cantor space *X* which may be realized as the simplex of all invariant probability measures for some minimal homeomorphism *g* of *X*. This extends a result of Akin for the case when *K* is a singleton, and an unpublished result of Dahl when *K* is finite-dimensional. All relevant notions of topological dynamics will be recalled. (Joint work with Tomás Ibarlucia).

# Analysis Seminar -- Discrete uniformization via hyper-ideal circle patterns

In this talk I will present a discrete version of the classical uniformization theorem based on the theory of hyper-ideal circle patterns. It applies to surfaces represented as finite branched covers over the Riemann sphere as well as to compact polyhedral surfaces with non-positive cone singularities. The former include all Riemann surfaces realized as algebraic curves, and more generally, any closed Riemann surface with a choice of a meromorphic function on it. The latter include any closed Riemann surface with a choice of a quadratic differential on it. We show that for such surfaces discrete uniformization via hyper-ideal circle patterns always exists and is unique (up to isometry). This kind of discrete uniformization is the result of an interplay between realization theorems for ideal (Rivin) and hyper-ideal (Bao and Bonahon) polyhedra in hyperbolic three-space, and their generalization to hyper-ideal circle patterns on surfaces with cone-singularities (Schlenker). We also propose a numerical algorithm, utilizing convex optimization, that constructs the desired discrete uniformization.

# Analysis Seminar -- The chemical distance in critical percolation

# The simplex of invariant measures of a minimal homeomorphism

We give a characterization of all simplices of probability measures on a Cantor space *X* which may be realized as the simplex of all invariant probability measures for some minimal homeomorphism *g* of *X*. This extends a result of Akin for the case when *K* is a singleton, and an unpublished result of Dahl when *K* is finite-dimensional. All relevant notions of topological dynamics will be recalled.

(Joint work with Tomás Ibarlucia)

# Colloquium Colloque des sciences mathématiques du Québec -- Random walks in random environments

The goal of this talk is to present some recent developments in the field of random walks in random environments. We chose to do this by presenting a specific model, known as biased random walk on Galton-Watson trees, which is intuitively easy to understand but gives rise to many interesting and challenging questions. We will then explain why this model is actually representative of a whole class of models which exhibit universal limiting behaviours.

# The human factor issue in optimisation: Examples from food science

Complex systems approaches are an attractive way to model food systems, as it yield powerful tools to address challenging issues like multi-scales and big data issues. The specifics of food domain however raises the focus on another crucial issue that is what can be called the human factor. At every stage, actually, human expertise and decision making have a major importance for an efficient modeling of food systems. Dealing with this is not a simple and solved problem. This talk illustrates with examples some research in this direction.

Ce séminaire a été rendu possible grâce à la collaboration de Rx&D.

# Seminar Geometry-Topology -- The Laplacian flow in G_2 geometry

A key challenge in Riemannian geometry is to find Ricci-flat metrics on compact manifolds, which has led to fundamental breakthroughs, particularly using geometric analysis methods. All non-trivial examples of such metrics have special holonomy, and the only special holonomy metrics which can occur in odd dimensions must be in dimension 7 and have holonomy G_2. I will describe recent progress on a proposed geometric flow method, introduced by Bryant, for finding metrics with holonomy G_2.

This is joint work with Yong Wei.

# Seminar Geometric Group Theory -- Log-space conjugacy problem in Grigorchuk groups

The definition of the Grigorchuk group is deceptively simple: it is generated by several actions on an infinite binary tree. However, it satisfies many uncommon properties: for example it has intermediate growth, but is not finitely presentable. In that light, it is interesting to see that many of the classical computational problems are ``easy'' in the Grigorchuk group. The word problem is known to be ``easy'' and we prove the same of the conjugacy problem. Here ``easy'' means log-space (and hence polynomial-time) decidable. We will introduce the Grigorchuk group and the precise notion of log-space decidability in some detail, following which we will discuss algorithms for the solution of the above-mentioned problems

# Seminar Statistique Sherbrooke -- Estimation des quantiles basée sur les copules : application sur des données hydrologiques

Dans la première partie de la présentation, un petit résumé sur l'utilisation des quantiles dans le domaine de l'hydrologie sera présenté et ainsi qu'une revue de littérature sur les différents modèles suggérés dans les travaux antérieurs pour modéliser les quantiles inconditionnels et les quantiles conditionnels, citant la théorie des valeurs extrêmes, la régression des quantiles paramétriques et non-paramétriques. Dans la deuxième partie, une nouvelle approche pour l'estimation des quantiles conditionnels basée sur les copules sera présentée. L’idée principale de cette approche est de décrire le lien entre la fonction des quantiles conditionnels et la copule. Dans ce cadre, deux estimateurs sont proposés. Des résultats asymptotiques et des simulations seront présentés.