Tri :
Date
Editeur
Auteur
Titre
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Mark Pollicott - Dynamical Zeta functions (Part 3)
/ Fanny Bastien
/ Canal-u.fr
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Voir le résumé
indisponible Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, dynamics, institut fourier, summer school, number theory
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Matteo Novaga - Nonlocal isoperimetric problems
/ Fanny Bastien
/ Canal-u.fr
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Voir le résumé
indisponible Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation
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Mike Boyle - Nonnegative matrices : Perron Frobenius theory and related algebra (Part 3)
/ Fanny Bastien
/ Canal-u.fr
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Voir le résumé
Lecture
I. I’ll give a complete elementary presentation of the essential
features of the Perron Frobenius theory of nonnegative matrices for the
central case of primitive matrices (the "Perron" part). (The "Frobenius"
part, for irreducible matrices, and finally the case for general
nonnegative matrices, will be described, with proofs left to
accompanying notes.) For integer matrices we’ll relate "Perron numbers"
to this and Mahler measures. Lecture II. I’ll describe how the
Perron-Frobenius theory generalizes (and fails to generalize) to 1,2,... x 1,2,...
nonnegative matrices. Lecture III. We’ll see the simple, potent
formalism by which a certain zeta function can be associated to a
nonnegative matrix, and its relation to the nonzero spectrum of the
matrix, and how polynomial matrices can be used in this setting for
constructions and conciseness. Lecture IV. We’ll describe a natural
algebraic equivalence relation on finite square matrices over a semiring
(such as Z, Z_+, R, ... ) which refines the nonzero spectrum and is
related to K-theory. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, dynamics, institut fourier, summer school, number theory
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Paul Zimmermann - CADO-NFS
/ Fanny Bastien
/ Canal-u.fr
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Voir le résumé
indisponible Mot(s) clés libre(s) : mathématiques, colloques, Grenoble (Isère), institut fourier
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Rod Gover - Geometric Compactification, Cartan holonomy, and asymptotics
/ Fanny Bastien
/ Canal-u.fr
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Voir le résumé
Conformal compactification has long been recognised as an effective geometric framework for relating conformal geometry, and associated field theories ``at infinity'', to the asymptotic phenomena of an interior (pseudo-‐)-‐Riemannian geometry of one higher dimension. It provides an effective approach for analytic problems in GR, geometric scattering, conformal invariant theory, as well as the AdS/CFT correspondence of Physics. I will describe how the notion of conformal compactification can be linked to Cartan holonomy reduction. This leads to a conceptual way to define other notions of geometric compactification. The idea will be taken up, in particular, for the case of compactifying pseudo-‐ Riemannian manifolds using projective geometry. A new characterisation of projectively compact metrics will be given, and some results on their asymptotics near the conformal infinity. This is joint work with Andreas Cap. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis
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Valérie Berthé - Fractions continues multidimensionnelles et dynamique (Part 2)
/ Fanny Bastien
/ Canal-u.fr
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Voir le résumé
Le
but de cet exposé est de présenter des généralisations
multidimensionnelles des fractions continues et de l’algorithme
d’Euclide d’un point de vue systèmes dynamiques, en nous concentrant sur
les liens avec la numération et les substitutions. Nous allons
considérer principalement deux types de généralisations, à savoir, les
algorithmes définis par homographies, comme l’algorithme de
Jacobi-Perron, et les fractions continues associées aux algorithmes de
réduction dans les réseaux. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, dynamics, institut fourier, summer school, number theory
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Yuan-Pin Lee - Introduction to Gromov-Witten theory and the crepant transformation conjecture (Part 4)
/ Fanny Bastien
/ Canal-u.fr
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Voir le résumé
In these lectures, Gromov{Witten theory will be introduced, assuming only basic
moduli theory covered in the rst week of the School. Then the Crepant Transformation Conjecture
will be explained. Some examples, with emphasis on the projective/global cases, will be given.
Note: The construction of virtual fundamental class, which forms the foundation of the GW theory,
will be given in Jun Li's concurrent lectures and will not be explained here. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, courbes, institut fourier, summer school, Gromov-Witten
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Laurent Mazet - Some aspects of minimal surface theory (Part 2)
/ Pauline Martinet
/ Canal-u.fr
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Voir le résumé
In a
Riemannian 3-manifold, minimal surfaces are critical points of the area
functional and can be a useful tool to understand the geometry and the
topology of the ambient manifold. The aim of these lectures is to give
some basic definitions about minimal surface theory and present some
results about the construction of minimal surfaces in Riemannian
3-manifolds. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric analysis, metric geometry, topology
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Giovanni Alberti - Introduction to minimal surfaces and finite perimeter sets (Part 1)
/ Fanny Bastien
/ 15-06-2015
/ Canal-u.fr
Alberti Giovanni
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Voir le résumé
In
these lectures I will first recall the basic notions and results that
are needed to study minimal surfaces in the smooth setting (above all
the area formula and the first variation of the area), give a short
review of the main (classical) techniques for existence results, and
then outline the theory of Finite Perimeter Sets, including
the main results of the theory (compactness, structure
of distributional derivative, rectifiability). If time allows, I
will conclude with a few applications.
Mot(s) clés libre(s) : Grenoble, école d'été, mathématique, institut fourier, summer school, geometric measure theory, calculus of variation
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Giovanni Alberti - Introduction to minimal surfaces and finite perimeter sets (Part 5)
/ Fanny Bastien
/ 18-06-2015
/ Canal-u.fr
Alberti Giovanni
Voir le résumé
Voir le résumé
In these lectures I will first
recall the basic notions and results that are needed to study minimal
surfaces in the smooth setting (above all the area formula and the first
variation of the area), give a short review of the main (classical)
techniques for existence results, and then outline the theory of Finite
Perimeter Sets, including the
main results of the theory (compactness, structure of distributional
derivative, rectifiability). If time allows, I will conclude with a few
applications. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation
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