Seminario de Teoría Espectral


2016-12-01
17:00hrs.
Nicolas Popoff. Universidad de Burdeos, Francia
Ground State Energy of The Robin Laplacian in Corner Domains.
Sala 1
Abstract:
I will consider the problem of the asymptotics of the first eigenvalue for the Laplacian with Robin boundary condition, when the Dirichlet parameter gets large. I will focus on the case where the domain belongs to a general class of corner domains, and show that the asymptotics is given at first order by the minimization of a function, called "local energy", defined on the tangent geometries. A key quantity of our analysis is the infimum of the essential spectrum of the Robin Laplacian on a cone.  Then, using a multiscale analysis, we give an estimate of the remainder. I will also provide a more precise asymptotics when the domain is regular, using a semiclassical effective Hamiltonian defined on the boundary and involving the mean curvature.
http://www.mat.uc.cl/~graikov/seminar.html
2016-12-01
15:30hrs.
Radu Purice. Instutute of Mathematics, Romanian Academy of Sciences
Spectral Gaps for Periodic Hamiltonians in Slowly Varying Magnetic Fields.
Sala 1
Abstract:
I report on some work done in collaboration with H. Cornean and B. Helffer. We
consider a periodic Schrödinger operator in two dimensions, perturbed by a
weak magnetic field whose intensity slowly varies around a positive mean. We
show in great generality that the bottom of the spectrum of the corresponding
magnetic Schrödinger operator develops spectral islands  separated by gaps,
reminding of a Landau-level structure.
First, we construct an effective magnetic matrix which accurately describes
the low lying spectrum of the full operator. The construction of this
effective magnetic matrix does not require a gap in the spectrum of the
non-magnetic operator, only that the first and the second Bloch eigenvalues
never cross.
Second, we perform a detailed spectral analysis of the effective matrix using
a gauge-covariant magnetic pseudo-differential calculus adapted for slowly
varying magnetic fields.
http://www.mat.uc.cl/~graikov/seminar.html
2016-11-24
17:00hrs.
Werner Kirsch. Universidad de Hagen, Alemania
On The Eigenvalue Distribution Measure for Random Matrices and Random Schrödinger Operators
Sala 1
Abstract:
We discuss classical and recent results on the distribution of eigenvalues (density of states) for random matrices and compare them to results for random Schrödinger operators.
We discuss Wigner’s semicircle law and some of its generalizations and sketch a rather elementary proof.
http://www.mat.uc.cl/~graikov/seminar.html
2016-11-17
17:00hrs.
Nicolás Espinoza. Facultad de Matemáticas, PUC
Valores Propios Nulos del Operador de Pauli 2D de Campos Magnéticos Casi Periódicos.
Sala 1
Abstract:
Revisamos resultados anteriores del operador de Pauli 2D: el Teorema de Aharonov-Casher y resultados acerca del operador de campos magnéticos periódicos. Luego revisamos el problema para un campo magnético casi periódico y describimos el kernel del operador de Pauli en el caso de un campo magnético particular.
http://www.mat.uc.cl/~graikov/seminar.html
2016-11-10
17:00hrs.
Galina Levitina. University of New South Wales, Australia
The Principal Trace Formula and its Applications To Index Theory, Spectral Shift Function and Spectral Flow
Sala 1
Abstract:
Let ${A(t)}_{t\in R}$ be a one parameter family of self-adjoint operators on a separable Hilbert space $H$, that converges in norm resolvent sense to the asymptotes $A_\pm$. Consider the operator $D_A=d/dt+A(t)$ on the Hilbert space $L_2(R,H)$. Without any assumption on the spectra of the operators $A_\pm$ we prove trace formula for semigroup difference of $D_A$, which was proved initially by Robbin-Salamon under the assumption of purely discrete spectra of $A_\pm$. As a consequence of this trace formula we establish the connection between spectral shift function for the pair of the asymptotes $(A_+,A_-)$, index theory for the operator $D_A$ and the spectral flow for the family ${A(t)}_{t\in R}$ applicable for differential operators in higher dimensions. This talk is the significant extension of the results presented by Prof. Fedor Sukochev on the conference 'Spectral theory and Mathematical Physics', Santiago, 2014.


http://www.mat.uc.cl/~graikov/seminar.html
2016-11-03
17:00hrs.
Simone Murro. University of Regensburg, Germany
A Novel Way of Constructing Hadamard State in Absence of Symmetry
Sala 1
Abstract:
We give a functional analytic construction of algebraic states for CAR algebras on a globally hyperbolic Lorentzian manifold. We show that in Minkowski space we recover the vacuum state and when we couple the Dirac equation to a time-dependent external potential, which is smooth and decays faster than quadratically for large times, we obtain Hadamard states.

http://www.mat.uc.cl/~graikov/seminar.html
2016-09-29
17:00hrs.
Georgi Raikov. Facultad de Matemáticas, PUC
Comportamiento Asintótico de los Valores Propios Pequeños del Laplaciano de Krein Perturbado
Sala 1
Abstract:

Consideraremos el Laplaciano de Krein $K$ en un dominio acotado regular, perturbado por un multiplicador real $V$, que se anula en la frontera. Suponiendo que $V$ tiene un signo definido, vamos a discutir el comportamiento asintótico de la sucesión de valores propios de $K+V$ que tiende al origen. En particular, vamos a demostrar que el Hamiltoniano efectivo que determina el término asintótico principal, es el operador armónico de Toeplitz con símbolo $V$, unitariamente equivalente a un operador pseudodiferencial en la frontera.

Se trata de un trabajo en conjunto con Vincent Bruneau (Burdeos, Francia).


http://www.mat.uc.cl/~graikov/seminar.html
2016-09-15
17:00hrs.
Pablo Miranda. Facultad de Matemáticas, PUC
Singularidades de la Función de Corrimiento Espectral Para Un Hamiltoniano Magnético en el Semiplano.
Sala 1
Abstract:

En esta charla consideraremos el operador de Schrödinger $H$, con campo magnético constante, definido en un semi-plano y perturbado por un potencial $V$ que decae al infinito.  Como una posible extensión del problema de conteo de valores propios discretos de $H+V$, introduciremos la Función de Corrimiento Espectral. Probaremos que esta función es acotada en conjuntos compactos que no contienen a los valores de Landau y describiremos su comportamiento asintótico en las singularidades que se presentan  en estos valores. Para los resultados mostrados se considerará la condición de borde de Dirichlet. Resultados con la condición de Neumann también será discutidos.


http://www.mat.uc.cl/~graikov/seminar.html
2016-06-22
Rafael Tiedra de Aldecoa. P. Universidad Católica de Chile
Degree, Mixing, and Absolutely Continuous Spectrum of Cocycles With Values in Compact Lie Groups (Part 2)
Sala 1 de la Facultad de Matemáticas PUC a las 17 horas
2016-06-15
Rafael Tiedra de Aldecoa. Facultad de Matemáticas, PUC
Degree, Mixing, and Absolutely Continuous Spectrum of Cocycles With Values in Compact Lie Groups
sala 1 de la Facultad de Matemáticas a las 17:00 horas
2016-05-05
Christian Sadel. Facultad de Matemáticas, PUC
Sde Limits for Products of Random Matrices and Goe Statistics for Rescaled Anderson Models on Long Strips.
Sala 1 de la Facultad de Matemáticas PUC a las 17 horas .
2016-04-28
Carlos Villegas-Blas. Universidad Nacional Autónoma de México
Sobre Teoremas de Distribución Límite de Autovalores Para el Hidrógeno en Campos Eléctricos O Magnéticos Constantes.
Sala 1 de la Facultad de Matemáticas a las 17:00 Hrs.
2015-12-03
Giuseppe de Nittis. Facultad de Matemáticas, PUC
Topological Piezo-Currents in Graphene
Sala 1 - Facultad de Matemáticas a las 17:00 Hrs.
2015-11-19
Marcus Carlsson. Universidad de Lund, Suecia
Multidimensional Frequency Estimation Using General Domain Hankel and Toeplitz Operators
Sala 1 de la Facultad de Matemáticas a las 17:00 Hrs.
2015-11-12
Werner Kirsch. Universidad de Hagen, Alemania
On The Mathematics of Political Power
Sala 1 de la Facultad de Matemáticas a las 17:00 Hrs.
2015-11-05
Rafael Tiedra de Aldecoa. Facultad de Matemáticas, PUC
Spectral Properties of Horocycle Flows for Surfaces of Negative Curvature
Sala 1 de la Facultad de Matemáticas a las 17:00 Hrs.
2015-10-29
Erdal Emsiz. Facultad de Matemáticas, PUC
Difference Equation for The Heckman-Opdam Hypergeometric Function and its Confluent Whittaker Limit
Sala 1 de la Facultad de Matemáticas a las 17:00 Hrs.
2015-10-22
Søren Fournais. Aarhus University
The Semi-Classical Limit of Large Fermionic Systems
Sala 1 de la Facultad de Matemáticas a las 17:00 Hrs.
2015-10-15
Rafael Benguria. Instituto de Fisica, PUC
Energia del Estado Fundamental de Un Sistema de Polarones
Sala 1 de la Facultad de Matemáticas UC a las 17:00 Hrs
2015-08-27
Rafael Tiedra de Aldecoa. P. Universidad Católica de Chile
Spectral and Scattering Properties At Thresholds for The Laplacian in a Half-Space With a Periodic Boundary Condition
Sala 1 de la Facultad de Matemáticas UC a las 17:00 Hrs.