1,384 Works

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...

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...

​​​​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.

Concentration properties of dynamical systems

Sébastien Gouëzel
Concentration is an important property of independent random variable, showing that any reasonable function of such variables does not vary a lot around its mean. Observables generated by the iteration of a chaotic enough dynamical system often share a lot of properties with independent random variables. In this survey talk, we discuss several situations where one can prove concentration for them, in uniformly or non-uniformly hyperbolic situations. We also explain why such a property is...

Möbius randomness and dynamics six years later

Peter Sarnak
There have many developments on the disjointness conjecture of the Möbius (and related) function to topologically deterministic sequences. We review some of these highlighting some related arithmetical questions.

$L^2$ curvature for surfaces in Riemannian manifolds

Ernst Kuwert
For surfaces immersed into a compact Riemannian manifold, we consider the curvature functional given by the $L^{2}$ integral of the second fundamental form. We discuss an area bound in terms of the energy, with application to the existence of minimizers. This is joint work with V. Bangert.

Collective dynamics in life sciences - Lecture 2. The Vicsek model as a paradigm for self-organization: from particles to fluid via kinetic descriptions

Pierre Degond
Lecture 1. Collective dynamics and self-organization in biological systems : challenges and some examples. Lecture 2. The Vicsek model as a paradigm for self-organization : from particles to fluid via kinetic descriptions Lecture 3. Phase transitions in the Vicsek model : mathematical analyses in the kinetic framework.

Incidences in Cartesian products

Jozsef Solymosi
Various problems in additive combinatorics can be translated to a question about incidences in Cartesian products. A well known example is Elekes' treatment of the sum-product problem but there are many more applications of incidence bounds to arithmetic problems. I will review the classical applications and show some recent results.

Recognizable languages are Church-Rosser congruential

Volker Diekert
The talk is based on a joint work with Kufleitner, Reinhardt, and Walter. The result was presented first at ICALP 2012 in Warwick. It shows that for each recognizable language L there exist some finite confluent and length-reducing semi-Thue system S such that L is a finite union of congruence classes with respect to S. This settled a long standing conjecture in formal language theory which dates back to a JACM publication by McNaughton, Narendran...

Coloring graphs on surfaces

Louis Esperet
coloring problem#coloring map#coloring definition#four color theorem#planar graphs#graphs on surfaces#locally planar graphs#locally planar graphs with even faces#list-coloring of planar graphs#questions of the audience

Approximating freeness under constraints, with applications

Sorin Popa
I will discuss a method for constructing a Haar unitary $u$ in a subalgebra $B$ of a $II_1$ factor $M$ that’s “as independent as possible” (approximately) with respect to a given finite set of elements in $M$. The technique consists of “patching up infinitesimal pieces” of $u$. This method had some striking applications over the years: 1. vanishing of the 1-cohomology for $M$ with values into the compact operators (1985); 2. reconstruction of subfactors through...

Rough volatility from an affine point of view

Christa Cuchiero
We represent Hawkes process and their Volterra long term limits, which have recently been used as rough variance processes, as functionals of infinite dimensional affine Markov processes. The representations lead to several new views on affine Volterra processes considered by Abi-Jaber, Larsson and Pulido. We also discuss possible extensions to rough covariance modeling via Volterra Wishart processes. The talk is based on joint work with Josef Teichmann.

Peierls substitution for magnetic Bloch bands

Stefan Teufel
We consider the one-particle Schrödinger operator in two dimensions with a periodic potential and a strong constant magnetic field perturbed by slowly varying non-periodic scalar and vector potentials, $\phi(\varepsilon x)$ and $A(\varepsilon x)$ , for $\epsilon\ll 1$ . For each isolated family of magnetic Bloch bands we derive an effective Hamiltonian that is unitarily equivalent to the restriction of the Schrödinger operator to a corresponding almost invariant subspace. At leading order, our effective Hamiltonian can...

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....

On low temperature kinetic theory; spin diffusion, anyons, Bose Einstein condensates

Leif Arkeryd
To illustrate specifically quantum behaviours, the talk will consider three typical problems for non-linear kinetic models evolving through pair collisions at temperatures not far from absolute zero. Based on those examples, a number of differences between quantum and classical Boltzmann theory is discussed in more general term.

Sato-Tate axioms

Francesc Fité
This series of three talks is the first part of an introductory course on the generalized Sato-Tate conjecture, made in collaboration with Andrew V. Sutherland at the Winter School "Frobenius distributions on curves", celebrated in Luminy in February 2014. In the first talk, some general background following Serre's works is introduced: equidistribution and its connexion to L-functions, the Sato-Tate group and the Sato-Tate conjecture. In the second talk, we present the Sato-Tate axiomatic, which leads...

Studying affine Deligne Lusztig varieties via folded galleries in buildings

Petra Schwer
We present a new approach to affine Deligne Lusztig varieties which allows us to study the so called "non-basic" case in a type free manner. The central idea is to translate the question of non-emptiness and the computation of the dimensions of these varieties into geometric questions in the Bruhat-Tits building. All boils down to understand existence of certain positively folded galleries in affine Coxeter complexes. To do so, we explicitly construct such galleries and...

The category MF in the semistable case

Gerd Faltings
For smooth schemes the category $MF$ (defined by Fontaine for DVR's) realises the "mysterious functor", and provides natural systems of coeffients for crystalline cohomology. We generalise it to schemes with semistable singularities. The new technical features consist mainly of different methods in commutative algebra

Distributions of Frobenius of elliptic curves #1

Chantal David
In all the following, let an elliptic curve $E$ defined over $\mathbb{Q}$ without complex multiplication. For every prime $\ell$, let $E[\ell]= E[\ell](\overline{\mathbb{Q}})$ be the group of $\ell$-torsion points of $E$, and let $K_\ell$ be the field extension obtained from $\mathbb{Q}$ by adding the coordinates of the $\ell$-torsion points of $E $. This is a Galois extension of$\mathbb{Q}$ , andGal$(K_\ell/\mathbb{Q})\subseteq GL_2(\mathbb{Z}/\ell\mathbb{Z})$. Using the Chebotarev density theorem for the extensions $K_\ell/\mathbb{Q}$ associated to a given curve $E$,...

High performance climate modelling : mimetic finite differences, and beyond?

Thomas Dubos
Climate models simulate atmospheric flows interacting with many physical processes. Because they address long time scales, from centuries to millennia, they need to be efficient, but not at the expense of certain desirable properties, especially conservation of total mass and energy. Most of my talk will explain the design principles behind DYNAMICO, a highly scalable unstructured-mesh energy-conserving finite volume/mimetic finite difference atmospheric flow solver and potential successor of LMD-Z, a structured-mesh (longitude-latitude) solver currently operational...

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.

On the B-Semiampleness Conjecture

Enrica Floris
An lc-trivial fibration $f : (X, B) \to Y$ is a fibration such that the log-canonical divisor of the pair $(X, B)$ is trivial along the fibres of $f$. As in the case of the canonical bundle formula for elliptic fibrations, the log-canonical divisor can be written as the sum of the pullback of three divisors: the canonical divisor of $Y$; a divisor, called discriminant, which contains informations on the singular fibres; a divisor, called...

Time changes of stochastic processes: convergence and heat kernel estimates

Takashi Kumagai
In recent years, interest in time changes of stochastic processes according to irregular measures has arisen from various sources. Fundamental examples of such time-changed processes include the so-called Fontes-Isopi-Newman (FIN) diffusion and fractional kinetics (FK) processes, the introduction of which were partly motivated by the study of the localization and aging properties of physical spin systems, and the two- dimensional Liouville Brownian motion, which is the diffusion naturally associated with planar Liouville quantum gravity. This...

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