14/05/2012 |
Departamento de Matemáticas. Facultad de Matemáticas.
Semianario de Sistemas Dinámicos
Volume growth and entropy for partially hyperbolic diffeomorphisms
Radu Saghin
PUC-Valparaíso
USACH (sala por confirmar)
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Resumen: I will present an inequality between the metric entropy, Lyapunov exponents, and an invariant measuring the growth of the volume in the direction of the unstable foliation (the integrated volume growth of $W^u$) of a $C^1$ partially hyperbolic diffeomorphism. I will discuss some situations where this integrated volume growth is locally constant, and several applications.
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07/05/2012 |
Departamento de Matemáticas. Facultad de Matemáticas.
Seminario Conjunto de Sistemas Dinámicos de Santiago
Low-temperature phase transitions in the quadratic family
Daniel Coronel
Pontificia Universidad Católica de Chile
Sala 403 del edificio R5 (República 399, 4to. piso), UNAB
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We give the first example of a quadratic map having a phase transition after the first zero of the geometric pressure function.
This implies that several dimension spectra and large deviation rate functions associated to this map are not (expected to be) real analytic, in contrast to the uniformly hyperbolic case. The quadratic map we study has a non-recurrent critical point, so it is
non-uniformly hyperbolic in a strong sense. Joint work with Juan Rivera-Letelier.
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02/05/2012 |
Departamento de Matemáticas. Facultad de Matemáticas.
CHARLA INFORMAL
ECUACIONES DIFERENCIALES GEOMÉTRICAS
MARIEL SAEZ
Pontificia Universidad Católica de Chile
Sala 2 (Víctor Ochsenius) - Facultad de Matemáticas - 17:00 Hrs.
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19/04/2012 |
Departamento de Matemáticas. Facultad de Matemáticas.
Seminario de EDP y Teoría Espectral
Twisting versus bending in curved quantum waveguides
David Krejcirik
Nuclear Physics Institute, Czech Academy of Sciences
Sala 2 (Víctor Ochesenius) - Facultad de Matemáticas - 17:00 Hrs.
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Abstract:
We make an overview of spectral-geometric effects of twisting and bending in quantum waveguides modelled by the Dirichlet Laplacian in unbounded three-dimensional curved tubes of uniform cross-section. We focus on the existence of curvature-induced eigenvalues in bent tubes and Hardy-type inequalities in twisted tubes of non-circular cross-section. Consequences of the results on the large time behaviour of the heat semigroup are also discussed.
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18/04/2012 |
Departamento de Matemáticas. Facultad de Matemáticas.
CHARLA INFORMAL
Marchas aleatorias en medios aleatorios
Alejandro Ramirez
Pontificia Universidad Católica de Chile
Sala 2 (Víctor Ochsenius)- Facultad de Matemáticas - 17:00 hRS.
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22/03/2012 |
Departamento de Matemáticas. Facultad de Matemáticas.
Seminario de EDP y Teoría Espectral
Large time behaviour of heat kernels
Daniel Lenz
Friedrich-Schiller-Universität Jena
Sala 2 (Víctor Ochsenius) - Facultad de Matemáticas
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Abstract: We study long time behaviour of heat kernels and show convergence of the semigroup to the ground state and convergence of
suitably averaged logarithms of kernels to the ground state energy. The results hold for arbitrary selfadjoint positivity improving semigroups. This framework includes Laplace operator on manifolds, on graphs and on quantum graphs. (Joint work with Matthias Keller, Hendrik Vogt, Radoslaw Wojciechowski)
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22/03/2012 |
Departamento de Matemáticas. Facultad de Matemáticas.
Seminario de Probabilidad
Overlaps and Pathwise Localization in the Anderson Polymer Model
Francis Comets
Universite de Paris VII
Sala 2 (Víctor Ochsenius) - Facultad de Matemáticas
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Abstract: We consider large time behavior of typical paths under the Anderson polymer measure with space-time disorder . We establish that the polymer measure gives a macroscopic mass to a small neighborhood of a typical path, for parameter values outside the perturbative regime of the random walk. This is a truely pathwise approach to polymer localization, in contrast with existing results. The localization becomes complete as the product of diffusivity and temperature square vanishes, in the sense that the mass grows to 1. Joint work with Michael Cranston (UCI, USA).
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19/03/2012 |
Departamento de Matemáticas. Facultad de Matemáticas.
Curso
Homogenization with connections to large deviations of random walks and diffusions in a random environment
S.R. Srinivasa Varadhan
Universidad de Nueva York
Auditorio Ninoslav Bralic - 17:00 a 18:20 Hrs
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El curso tendrá tres sesiones los días 19, 20 y 21 de marzo, entre las 17:00 y 18:20 horas, y se realizará en el Auditorio Ninoslav Bralic de la Facultad de Matemáticas de la Pontificia Universidad Católica de Chile y está dirigido a académicos y estudiantes de postgrado |
16/03/2012 |
Departamento de Matemáticas. Facultad de Matemáticas.
Coloquio de Matemáticas
Automorphism groups of algebraic surfaces
Igor Dolgachev
University of Michigan
Auditorio Ninoslav de la PUC - 15:00 Hrs.
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Abstract: I will survey some recent and old results about automorphism groups of complex algebraic surfaces with special emphasis on rational, Enriques and K3 surfaces |
16/03/2012 |
Departamento de Matemáticas. Facultad de Matemáticas.
Coloquio de Matemáticas
The automorphism group of a T-variety of complexity one
Alvaro Liendo
Mathematisches Institut, Universitat Bern
Auditorio Ninoslav Bralic - 16:10 Hrs
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A T-variety is a normal variety endowed with a faithful action of the algebraic torus T=(k^*)^n. The complexity of a T-variety is the codimension of a generic orbit. The best known examples of T-varieties are toric varieties, i.e., T-varieties of complexity 0.
In the first part of this talk, we present a combinatorial description of T-varieties given by Almann, Hausen and Süss in 2006. This description generalizes the usual description of toric varieties by means of fans to higher complexity. In the second part of this talk, we will discuss a recent result where we compute the root system of the automorphism group of a rational complete T-variety of complexity one.
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12/03/2012 |
Departamento de Matemáticas. Facultad de Matemáticas.
Cursillo
Introduction to the theory of elliptic surfaces
Igor Dolgachev
University of Michigan
Auditorio Ninoslav Bralic - 16:00 Hrs.
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El cursillo se realizará los dias lunes 12, martes 13, miercoles 14 de marzo de 2012 a las 16:00 Hrs. en el Auditorio Ninoslav de la PUC.
Abstract: An elliptic surface is an algebraic surface which admits a fibration with a fibre an elliptic curve. An example of such a surface is the blow-up of base points of a pencil of plane cubic curves. Although a general fibre is a nonsingular curve, some fibres can be singular, and their classification reveals a surprising relationship with Dynkin diagrams of simple Lie algebras. I will try to be non-technical, explaining most of the theory for the case of pencils of plane cubic curves, and their generalizations, Halphen pencils of plane elliptic curves of degree 3m with 9 m-multiple singular points. The theory of such pencils is ultimately related to old problem in algebraic geometry: finding a geometric construction of fake projective planes.
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08/03/2012 |
Departamento de Matemáticas. Facultad de Matemáticas.
CHARLA MOTIVACIONAL
What is algebraic geometry about
Igor Dolgachev
University of Michigan
Auditorio Ninoslav Bralic - Facultad de Matemáticas - 15:15 Hrs.
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05/03/2012 |
Departamento de Matemáticas. Facultad de Matemáticas.
Seminario de Sistemas Dinámicos
Transience in Dynamical Systems
Mike Todd
University of St. Andrews (Escocia)
Sala 1, facultad de Matematicas, PUC
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23/01/2012 |
Departamento de Matemáticas. Facultad de Matemáticas.
Seminario SCS-D de Sistemas Dinámicos de Santiago
Some advances on the selection problem
Renaud Leplaideur
Université de Brest, Francia
Sala 2 (Víctor Ochsenius) Facultad de Matemáticas UC- 16:30 Hrs.
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I will present the problem of selection at temperature zero. Given a Dynamical System $X$ and $f o X$ and a potential $phi$ we look for the $f$-invariant measures $mu$ which maximize $int phi,dmu$. Such a measure is called a $phi$-maximizing measure. On the other hand, the Thermodynamical formalism produces an Equilibrium State $mu_eta$ for the potential $etaphi$ with $eta>0$. A ground state for $phi$ is a $phi$-maximizing measure which is an accumulation point for $mu_eta$ as $eta$ goes to $+infty$. The selection problem is to determine if $mu_eta$ converges, and also how it chooses the limit between all the $phi$-maximizing measures. The convergence does not always occur, but it turns out that fore some potentials, it is possible to prove convergence and to determine the limit. The talk will recall part of the background needed to understand and present the problem and will show some results. In particular, we emphasize that the Max-Plus formalism seems to be a powerful tool to solve the problem.
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19/01/2012 |
Departamento de Matemáticas. Facultad de Matemáticas.
Seminario de Probabilidad
Survival probability of the branching random walk killed below a linear boundary
Jean Berard
Jean Berard
Sala 3 (sector postgrado) - Facultad de Matemáticas - 16:30 Hrs.
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