Seminar Spectral Theory and PDE

Seminar Spectral Theory and PDE, May 16, 17:00

Frédéric Klopp. Institut de Mathématiques Jussieu – Paris Rive Gauche, Sorbonne
Title: Exponential decay for the 2 particle density matrix of disordered many-body fermions at zero and positive temperature.
Place: Pontificia Universidad Católica de Chile, Facultad de Matemáticas (campus San Joaquin), Sala 2
Abstract:
We will consider a simple model for interacting fermions in a random background at zero and positive temperature. At zero temperature, we prove exponential decay for the 2 particle density matrix of a ground state. At positive temperature we prove exponential decay for the 2 particle density matrix of the density operator in the grand canonical ensemble.
http://www.mat.uc.cl/~graikov/seminar.html

Announcement, conference

2nd JNMP Conference on Nonlinear Mathematical Physics: 2019

The 2nd JNMP Conference on Nonlinear Mathematical Physics: 2019 conference is held from May 26 till June 4, 2019 at the University of Santiago de Chile.
USACH – Centro de estudios de postgrado y educación continua 
(Center for postgraduate studies and continuing education) 
Piso 3, Av. Apoquindo 4499, Las Condes, Región Metropolitana, Santiago, Chile

Description

This conference is being organized for the Journal of Nonlinear Mathematical Physics (JNMP) community. We aim to bring together experts and young scientists in the area of Mathematical Physics that concern Nonlinear Problems in Physics and Mathematics. The main topic of the conference is centered around the scope of JNMP: continuous and discrete integrable systems including ultradiscrete systems, nonlinear differential- and difference equations, applications of Lie transformation groups and Lie algebras, nonlocal transformations and symmetries, differential-geometric aspects of integrable systems, classical and quantum groups, super geometry and super integrable systems.

seminar FisMat

FisMat Seminar, May 15, 15:45

Massimo Moscolari. Aalborg University
Title: Beyond Diophantine Wannier diagrams: gap labelling for Bloch-Landau Hamiltonians
Place: Pontificia Universidad Católica, Facultad de Matemáticas (Campus San Joaquin), Sala 5
Abstract:
In 1978 Wannier discovered a Diophantine relation expressing the integrated density of states of a gapped group of bands of the Hofstadter Hamiltonian as a linear function of the magnetic field flux with integer slope. I will show how to extend this relation to a gap labelling theorem for any 2D Bloch-Landau Hamiltonian operator and to certain non-covariant systems having slowly varying magnetic fields. The integer slope will be interpreted as the Chern character of the projection onto the space of occupied states. The talk is based on a joint work with H. Cornean and D. Monaco.

Seminar Spectral Theory and PDE

Seminar Spectral Theory and PDE, May 2, 17:00

Georgi Raikov. Pontificia Universidad Católica de Chile
Title: Threshold singularities of the spectral shift function for geometric perturbations of a magnetic Hamiltonian
Place: Pontificia Universidad Católica de Chile, Facultad de Matemáticas (campus San Joaquin), Sala 2
Abstract:
I will consider the 3D Schrödinger operator H0 with constant magnetic field, and its perturbations H_+ (resp., H_-\, ) obtained from H_0  by imposing Dirichlet (resp., Neumann) conditions on an appropriate surface. I will introduce the Krein spectral shift function for the operator pairs (H_0;H_+) and (H_0;H_-), and will discuss its singularities at the Landau levels which play the role of thresholds in the spectrum of the unperturbed operator H_0
The talk is based on a joint work with V. Bruneau (Bordeaux).
http://www.mat.uc.cl/~graikov/seminar.html

seminar FisMat

FisMat Seminar, April 24, 15:45

Svetlana Jitomirskaya. University of California, Irvine
Title: Cantor spectrum of a model of graphene in magnetic field
Place: Pontificia Universidad Católica de Chile, Facultad de Matemáticas (Campus San Joaquin), Sala 5
Abstract:
We consider a quantum graph as a model of graphene in magnetic fi elds and give a complete analysis of the spectrum, for all constant fluxes. In particular, we show that if the reduced magnetic flux  through a honeycomb is irrational, the continuous spectrum is an unbounded Cantor set of Lebesgue measure zero and Hausdorff dimension bounded by 1/2.

Based on joint works with S. Becker, R. Han, and also I. Krasovsky

doctoral schools

Spring School in Analysis and Mathematical Physics, October 14-22, 2019

From October 14 to 22, we will have the Spring School in Analysis and Mathematical Physics in Santiago at the Pontificia Universidad Católica de Chile. The school is directed to undergraduate and graduate students.

– Oficial website of the Doctoral School in english –
– Página oficial de la Escuela Doctoral en español –

Program

We will have 4 courses, each one composed of 3 sessions of 90 minutes:

Moreover, there will be additional talks, tutorial classes, and a presentation of our graduate program.

Fellowship / Registration

There will be fellowships available for travel cost and accommodation in Santiago. Interested students can register and apply for the fellowships here.
If you apply for a fellowship, please send a printout (pdf file) of your latest courses and grades to escueladoc@mat.uc.cl.

Tentative Schedule

Weak 1, October 14-18

 Mo
14.10.
Tu
15.10.
We
16.10.
Th
17.10.
Fr
18.10.
9:00-9:30Welcome
9:30-11:00Course 1Course 1Course 2Course 1Course 4
11:00-11:30coffeecoffeecoffeecoffeecoffee
11:30-1:00Course 2Course 2Course 3Course 3Course 4
1:00-2:00lunchlunchlunchlunchlunch
2:00-3:00Course 3Talk 1Talk 2Talk 3tutorial
3:00-3:30coffeecoffeecoffee
3:30-4:00coffeetutorialtutorialtutorialcoffee
4:00-5:00Presentation
graduate program
Club de
Matematica

Weak 2, October 21-22

 Mo
21.10.
Tu
22.10.
10:00-11:00Talk 4Talk 5
11:00-11:30coffeecoffee
11:30-1:00Course 4tutorial,
hand in homework
1:00-2:00lunchlunch
2:00-3:00interviewsTalk 6
3:00-3:30coffeecoffee
3:30-5:00interviewshomework discussion
5:00-7:00BBQ

Organizers


Announcement

Position in Mathematical Physics at the Institute of Physics at PUC Chile

The Institute of Physics at Pontificia Universidad Católica de Chile invites applications for a tenure-track faculty position in Mathematical Physics at the Assistant Professor level, to start as early as August 2019. A Ph.D. degree in Physics (or closely related areas) is required and postdoctoral experience is highly desirable. We are looking for candidates having the potential of interaction with the established research areas in Mathematical Physics at the institute such as Analysis, PDE, Quantum Physics, and Non-linear Physics.
The successful candidate is expected to establish a leading research program as well as to teach in Spanish at the undergraduate and graduate levels.
Applications must include two recommendation letters, curriculum vitae, list of publications, and statements of past and proposed research and teaching interests. The two recommendation letters must be sent separately to the application’s e-mail address. All the documents should be sent by email before April 30, 2019 to the Head of the Search Committee at concurso2019@fis.puc.cl


seminar FisMat

FisMat Seminar, April 17, 15:45

Walter de Siqueira Pedra. University of São Paulo
Thermodynamical Stability and Dynamics of Lattice Fermions with Mean-Field Interactions
Place: Pontificia Universidad Católica, Facultad Matemáticas (Campus San Joaquin) Sala 5
Abstract:
For lattice fermions we study the thermodynamic limit of the time evolution of observables when the corresponding finite-volume Hamiltonians contain mean-field terms (like, e.g., the BCS model). It is well-known that, in general, this limit does not exist in the sense of the norm of observables, but may exist in the strong operator topology associated to a well-chosen representation of the algebra of observables. We proved that this is always the case for any cyclic representation associated to an invariant minimizer of the free energy density, if the Hamiltonians are invariant under translations. Our proof uses previous results on the structure of states minimizing the free energy density of mean-field models along with Lieb-Robinson bounds for the corresponding families of finite-volume time evolutions. This is a joint work with Jean-Bernard Bru, Sébastien Breteaux and Rafael Miada.