1,623 Works

Automorphisms of curve and pants complexes in profinite content

Louis Funar
Pants complexes of large surfaces were proved to be vigid by Margalit. We will consider convergence completions of curve and pants complexes and show that some weak four of rigidity holds for the latter. Some key tools come from the geometry of Deligne Mumford compactification of moduli spaces of curves with level structures.

Interview at CIRM: Dusa McDuff

Dusa McDuff
Dusa McDuff is the Helen Lyttle Kimmel '42 Professor of Mathematics at Barnard College. At Barnard, she currently teaches "Calculus I", "Perspectives in Mathematics" and courses in geometry and topology. Professor McDuff gained her early teaching experience at the University of York (U.K.), the University of Warwick (U.K.) and MIT. In 1978, she joined the faculty of the Department of Mathematics at SUNY Stony Brook, where she was awarded the title of Distinguished Professor in...

​On Hitchin’s hyperkähler metric on moduli spaces of Higgs bundles

Andrew Neitzke
I will review a conjecture (joint work with Davide Gaiotto and Greg Moore) which gives a description of the hyperkähler metric on the moduli space of Higgs bundles, and recent joint work with David Dumas which has given evidence that the conjecture is true in the case of $SL(2)$-Higgs bundles.

​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...

Darcy problem and crowd motion modeling

Bertrand Maury
We describe here formal analogies between the Darcy equations, that describe the flow of a viscous fluid in a porous medium, and some problems arising from the handing of congestion in crowd motion models. At the microscopic level, individuals are identified to rigid discs, and the dual handling of the non overlapping constraint leads to discrete Darcy-like equations with a unilateral constraint that involves the velocities and interaction pressures, and that are set on the...

Establishment in a new habitat under the infinitesimal model

Alison M. Etheridge & Nicholas H. Barton
Maladapted individuals can only colonise a new habitat if they can evolve a positive growth rate fast enough to avoid extinction - evolutionary rescue. We use the infinitesimal model to follow the evolution of the growth rate, and find that the probability that a single migrant can establish depends on just two parameters: the mean and genetic variance of fitness. With continued migration, establishment is inevitable. However, above a threshold migration rate, the population may...

A Jacobian criterion for smoothness of algebraic diamonds

Laurent Fargues
(joint work with Peter Scholze) In our joint work with Scholze we need to give a meaning to statements like "the stack of principal G-bundles on the curve is smooth of dimension 0" and construct "smooth perfectoid charts on it". The problem is that in the perfectoid world there is no infinitesimals and thus no Jacobian criterion that would allow us to define what is a smooth morphism. The good notion in this setting is...

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.

Cohomology and $L^2$-Betti numbers for subfactors and quasi-regular inclusions

Stefaan Vaes
I present a joint work with S. Popa and D. Shlyakhtenko introducing a cohomology theory for quasi-regular inclusions of von Neumann algebras. In particular, we define $L^2$-cohomology and $L^2$-Betti numbers for such inclusions. Applying this to the symmetric enveloping inclusion of a finite index subfactor, we get a cohomology theory and a definition of $L^2$-Betti numbers for finite index subfactors, as well as for arbitrary rigid $C^²$-tensor categories. For the inclusion of a Cartan subalgebra...

La bibliothèque demain

Louis Klee
introduction#état des lieux#quel avenir ?#nouveaux modes de fabrication et transmission des savoirs#perspectives techniques#perspectives économiques#perspectives sociétales 1#perspectives sociétales 2#perspectives et ressources humaines#la bibliothèque pilier de la démocratie numérique ?#questions de l'auditoire

Stability and applications to birational and hyperkaehler geometry - Lecture 1

Arend Bayer
This lecture series will be an introduction to stability conditions on derived categories, wall-crossing, and its applications to birational geometry of moduli spaces of sheaves. I will assume a passing familiarity with derived categories. - Introduction to stability conditions. I will start with a gentle review of aspects of derived categories. Then an informal introduction to Bridgeland’s notion of stability conditions on derived categories [2, 5, 6]. I will then proceed to explain the concept...

Multi-level mathematical models for cell migration in dense fibrous environments

Luigi Preziosi
Cell-extracellular matrix interaction and the mechanical properties of cell nucleus have been demonstrated to play a fundamental role in cell movement across fibre networks and micro-channels and then in the spread of cancer metastases. The lectures will be aimed at presenting several mathematical models dealing with such a problem, starting from modelling cell adhesion mechanics to the inclusion of influence of nucleus stiffness in the motion of cells, through continuum mechanics, kinetic models and individual...

Height pairings, torsion points, and dynamics

Holly Krieger
We will present work in progress, joint with Hexi Ye, towards a conjecture of Bogomolov, Fu, and Tschinkel asserting uniform bounds for common torsion points of nonisomorphic elliptic curves. We introduce a general approach towards uniform unlikely intersection bounds based on an adelic height pairing, and discuss the utilization of this approach for uniform bounds on common preperiodic points of dynamical systems, including torsion points of elliptic curves.

Interview at CIRM: Pavel Exner

Pavel Exner
Pavel Exner from the Academy of Sciences of the Czech Republic in Prague is president of the European Mathematical Society (2015-2018). He's currently also the scientific director at the Doppler Institute for Mathematical Physics and Applied Mathematics in Prague.

Interview au CIRM : Virginie Bonnaillie Noël

Virginie Bonnaillie-Noël
Directrice de recherche CNRS au DMA, UMR 8553 (équipe Analyse) Directrice Adjoint Scientifique à l'Insmi, en charge de la politique de sites (Institut des Sciences Mathématiques et de leurs Interactions - CNRS) Adjointe Déléguée Scientifique Référente au CNRS

Rare event simulation for molecular dynamics

Arnaud Guyader
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...

Inhomogeneities and temperature effects in Bose-Einstein condensates

Anne De Bouard
We will review in this talk some mathematical results concerning stochastic models used by physicist to describe BEC in the presence of fluctuations (that may arise from inhomogeneities in the confinement parameters), or BEC at finite temperature. The results describe the effect of those fluctuations on the structures - e.g. vortices - which are present in the deterministic model, or the convergence to equilibrium in the models at finite temperature. We will also describe the...

Interview at CIRM: Dipendra Prasad

Dipendra Prasad
Jean-Morlet Chair 2016: Cirm is delighted to welcome Dipendra Prasad (Tata Institute of Fundamental Research in Mumbai) and Volker Heiermann (I2M Marseille) for six months. Five scientific events are scheduled at CIRM between January and June 2016 and a range of worldwide guests will be invited over this period. CIRM - Chaire Jean-Morlet 2016 - Aix-Marseille Université

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.

​​​​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.

Economic cycles: from descriptive statistics to formalization

Michel Armatte
In order to explore the advances made on the economic issue of business cycles, I will present the work of the American economist Henry Ludwell Moore, who published four works on the question between the years 1911 and 1923. Within this framework, I will introduce several issues, such as the duality of empirical and theoretical approaches, the causal and semiological interpretations of the correlation, the notion of the ceteris paribus law in economics, the notion...

Was the Russian theory of cycles a mathematical theory?

Irina Konovalova-Peaucelle
Cournot Centre session devoted to the transformations that took place in mathematical economics during the interwar period.

Mathematical economics after first world war: round table discussion

Pierre-Charles Pradier, Michel Armatte, Irina Konovalova-Peaucelle & Jean-Philippe Touffut
Cournot Centre session devoted to the transformations that took place in mathematical economics during the interwar period.

Compressed sensing and high-dimensional approximation: progress and challenges

Ben Adcock
Many problems in computational science require the approximation of a high-dimensional function from limited amounts of data. For instance, a common task in Uncertainty Quantification (UQ) involves building a surrogate model for a parametrized computational model. Complex physical systems involve computational models with many parameters, resulting in multivariate functions of many variables. Although the amount of data may be large, the curse of dimensionality essentially prohibits collecting or processing enough data to reconstruct such a...

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