Seminario EDP y Teoría Espectral


2015-11-16
Matteo Rizzi. Sissa, Italy
Clifford Tori and The Singularly Perturbed Cahn-Hilliard Equation
Seminarios del 5to. piso del DIM a partir de las 16:00 hrs.
2015-11-16
Panayotis Smyrnelis. (Cmm)
Connecting Orbits of The System $U”= Abla W(U)$
Sala de Seminarios del 5to. piso del DIM a partir de las 17:10 hrs.
2015-11-02
Phuoc-Tai Nguyen. Facultad de Matemáticas, Pontificia Universidad Católica de Chile),
Nonlinear Elliptic Equations With Absorption Term and Measure Boundary Data
Sala 5 de la Facultad de Matemáticas UC a las 16:00 Hrs.
2015-11-02
Rafael Benguria. Departamento de Física, Pontificia Universidad Católica de Chile
The Brezis-Nirenberg Problem on S^n, in Spaces of Fractional Dimension
Sala 5 Facultad de Matemáticas PUC a las 16:00 Hrs.
2015-10-19
Rémy Rodiac. Rémy Rodiac
Ginzburg-Landau Type Problems With Prescribed Degrees on The Boundary
Sala 5 Facultad de Matemáticas PUC a las 16:00 Hrs.
2014-06-18
Matías Courdurier. P. Universidad Católica de Chile
Mathematical Aspects of Image Reconstruction Using Scattering in Spect Medical Imaging.
Sala 1 de la Facultad de Matemáticas - 17:00 Hrs.
2014-06-04
Monica Musso. P. Universidad Católica de Chile
Non Degeneracy of Sign Changing Entire Solutions for The Yamabe Equation in R^n
Sala 1 - Facultad de Matemáticas UC - 17:00 Hrs.
2012-10-18
Rafael Tiedra. Pontificia Universidad Católica de Chile
Time Delay and Calabi Invariant in Classical Scattering Theory
Sala 2 (Víctor Ochesenius) - Facultad de Matemáticas - 17:00 Hrs.
Abstract:
Resumen: We define, prove the existence and obtain explicit expressions for classical time delay defined in terms of sojourn times for abstract scattering pairs (H_0,H) on a symplectic manifold. As a by-product, we establish a classical version of the Eisenbud-Wigner formula of quantum mechanics. Using recent results of V. Buslaev and A. Pushnitski on the scattering matrix in Hamiltonian mechanics, we also obtain an explicit expression for the derivative of the Calabi invariant of the Poincaré scattering map. Our results are applied to dispersive Hamiltonians, to a classical particle in a tube and to Hamiltonians on the Poincaré ball.

2012-10-04
Rafael Tiedra. Pontificia Universidad Católica de Chile
Commutator Methods for Unitary Operators
Sala 2 (Víctor Ochesenius) - Facultad de Matemáticas - 17:00 Hrs.
Abstract:
We present an improved version of commutator methods for unitary operators under a weak regularity condition. Once applied to a unitary operator, the method typically leads to the absence of singularly continuous spectrum and to the local finiteness of point spectrum. Some applications for Floquet operators and for cocycles over irrational rotations will be presented.

2012-07-05
Serge Richard. Universidad Lyon I, Francia
Low Energy Spectral and Scattering Theory for Relativistic Schroedinger Operators
Sala 2 (Víctor Ochesenius) - Facultad de Matemáticas - 17:00 Hrs.
2012-04-19
David Krejcirik. Nuclear Physics Institute, Czech Academy of Sciences
Twisting Versus Bending in Curved Quantum Waveguides
Sala 2 (Víctor Ochesenius) - Facultad de Matemáticas - 17:00 Hrs.
Abstract:
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.

2012-03-22
Daniel Lenz. Friedrich-Schiller-Universität Jena
Large Time Behaviour of Heat Kernels
Sala 2 (Víctor Ochsenius) - Facultad de Matemáticas
Abstract:
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)


2011-11-24
Serge Richard. University of Tsukuba, Japan
Positive Quantization in The Presence of a Variable Magnetic Field
Sala 2 (Víctor Ochsenius) - Facultad de Matemáticas - 17:00 Hrs.
Abstract:
Abstract:
During this seminar, we shall first recall some known results on the magnetic Weyl calculus. Then, based on a family of magnetic coherent states, we shall introduce a Berezin quantization for a particle in a variable magnetic field and we show that it constitutes a strict quantization of a natural Poisson algebra.

2011-11-17
Amal Attouchi. Universidad de Paris 13, Francia
Comportamiento Local y Global de Las Soluciones de la Ecuación de Hamilton-Jacobi Con Operador de Difusión No Lineal
Sala 2 (Víctor Ochsenius) - Facultad de Matemáticas - 17:00 Hrs.
2011-10-27
Georgi Raikov. Pontificia Universidad Católica de Chile
Fórmula de Traza Para el Operador de Landau Perturbado
Sala 2 (Víctor Ochsenius) - Facultad de Matemáticas - 17:00 Hrs.
Abstract:
Se presentará una fórmula de traza para los cúmulos de valores propios del operador de Landau, es decir el operador bidimensional de Schrödinger con campo magnético constante, perturbado por un potencial eléctrico que decae al infinito. El espectro de este operador consiste en cúmulos de valores propios discretos que se acumulan en los niveles de Landau. Se estudiará la densidad asintótica de los valores propios dentro de estos cúmulos cuando el número del cúmulo tiende hacia el infinito. Esta densidad asintótica será descrita explícitamente en términos de la transformada de Radon del potencial perturbativo. Las herramientas usadas en las demostraciones de los resultados principales incluyen métodos relativos a la teoría de operadores de Berezin-Toepli
2011-10-06
Alberto Montero. Pontificia Universidad Católica de Chile
la Energía de Ginzburg Landau de Una Función Bien Localizada
Sala 2 (Víctor Ochsenius) - Facultad de Matemáticas - 17:00 Hrs.
Abstract:
En esta charla voy a hablar de la energía de Ginzburg-Landau de una función definida en un dominio suave en R{3}, a valores complejos, cuyos conjuntos de nivel están cerca en promedio de una curva dada.

2011-09-15
Alex Sobolev. University College London, Uk
Discrete Spectrum Asymptotics for Certain Finite Band Lattice Operators
Sala 2 (Víctor Ochsenius) - Facultad de Matemáticas - 17:00 horas
Abstract:
Discrete spectrum asymptotics have been extensively studied for classical Jacobi matrices with the dominating growing diagonal part. We obtain analogous asymptotic formulas for multidimensional finite band lattice operators. The central idea of the method goes back to the Near Diagonalization Approach by G. Rozenblum, but the multi-dimensional nature of the problem leads to the occurrence of resonant zones" in the lattice, which make the asymptotic properties of these operators more involved than in the one-dimensional case. The accurate description of the resonant zones is the main technical difficulty of this work"
2011-09-01
Rafael Tiedra de Aldecoa. Pontificia Universidad Católica de Chile
Two-Hilbert Spaces Mourre Theory for The Laplace-Beltrami Operator on Manifolds With Asymptotically Cylindrical Ends
Sala 2 (Víctor Ochsenius) - Facultad de Matemáticas PUC - 17:00 HRS.
Abstract:
We review some aspects of Mourre theory in a two-Hilbert spaces setting. Then we apply this theory to the spectral analysis for the Laplace-Beltrami operator on manifolds with asymptotically cylindrical ends.
This is a joint work with Serge Richard (University of Tsukuba).

2011-07-27
Cedric Meresse. Cpt, Marseille
Normal Form for Some Time-Independent Magnetic Hamiltonians
Sala 2 (Víctor Ochsenius) - 17:00 Hrs. Facultad de Matemáticas - UC
Abstract:
In this talk, we will discuss the existence of a normal form for some time independent quantum magnetic systems. First, we look at systems which have a quadratic perturbations. Then, we will focus our interest on more general systems using a partial diagonalization algorithm
2011-05-25
Erdal Emsiz. Pontificia Universidad Católica de Chile
El Ansatz de Bethe en Una Alcoba de Weyl
Sala 2 (Víctor Ochsenius) - Facultad de Matemáticas - 17:00 Hrs.
Abstract:
En esta charla voy a hablar sobre sistemas de raíces (de las álgebras de Lie semi-simples complejas) versiones de partículas cuánticas en una dimensión en el círculo con potencial de delta repulsivo. Una parte importante de esta charla se dedicará al describir cómo resolver el problema espectral con el Ansatz de Bethe. Además, las funciones propias de Bethe son completas, en el sentido de que su span lineal es denso en el espacio de Hilbert de las funciones cuadráticas en una alcoba de Weyl. También hablaré sobre una fórmula (conjetural)determinante compacta para las normas cuadráticas de las funciones propias de Bethe. Si hay tiempo también hablaré sobre la relación con álgebras de Hecke afines de dichos sistemas