The Pan-American Advanced Studies Institute, 2006 (PASI) on Analysis and Probability in Quantum Physics will be held at Pontificia Universidad Católica de Chile, Santiago de Chile, 24 July--4 August, 2006.

The Institute will emphasize the use of probability theory and analysis in modern mathematical physics, in areas such as random Schrödinger and wave operators, the stability of matter, and quantum transport theory. The two week program will consist of a series of six mini-courses during the first week and an international workshop the second week.

INTERNATIONAL ORGANIZING COMMITTEE

CHAIR OF ORGANIZING COMMITTEE
Peter D. Hislop, Mathematics Department, University of Kentucky

The members of the committee represent the various areas of concentration of the PASI program. The Organizing Committee also assist the PI with advertising the PASI meeting, and in the selection of the students for the school.

COMMITTEE MEMBERS
Horacio Falomir, Universidad Nacional de La Plata, La Plata, Argentina
Claudio Fernandez, Pontificia Universidad Católica de Chile, Santiago de Chile
Alejandro Ramirez, Pontificia Universidad Católica de Chile, Santiago de Chile
Georgi Raikov, Universidad de Chile, Santiago de Chile
Ricardo Weder, Universidad Nacional Autonoma de Mexico, Mexico City, Mexico

COMMITTEE MEMBERS' EXPERIENCE
Horacio Falomir is an expert in quantum field theory and spectral theory.
Claudio Fernandez is an expert on resonances and geometric scattering.
Alejandro Ramirez is an expert in probability theory and its application
to random media and interacting particle systems. He organized the meeting "Percolation, Particle Systems, and Random Media" in Santiago de Chile in January 2004.
Georgi Raikov is a specialist in the spectral theory of Schrödinger operators, especially Schrödinger operators with magnetic fields.
Ricardo Weder is a specialist in scattering and inverse scattering theory. He was involved in the organization of a PASI program on inverse problems in November, 2001.

WEEK ONE: Mini-courses, 24--28 July 2006

We plan to support up to 40 students from the Americas so that they may attend the PASI school and workshop. If our requests to other agencies are funded, we will be able to invite more students. There will be 6 mini-courses of 4-lecture hours per course. We have chosen topics that are at the center of contemporary research in the mathematical theory of quantum mechanics.

LECTURE TOPICS AND PRESENTERS

Ira W. Herbst, University of Virginia,
The Spectral and Scattering Theory of Quantum Particles in External Fields.

Abel Klein, University of California, Irvine
Random Schrödinger Operators.

Jean Bellissard, Georgia Institute of Technology
Theory of Quantum Transport.

H. T. Yau, Stanford University
Probabilistic Methods in Mathematical Physics.

Richard Froese, University of British Columbia
Theory of Quantum Resonances.

Rafael Benguria, Pontificia Universidad Católica de Chile
Stability of Matter and Quantum Field Theory.

LINK TO BIOGRAPHICAL SKETCH OF SPEAKERS:

Ira W. Herbst is professor of mathematics and department chair at the University of Virginia. He is an expert in the quantum N-body problem, properties of eigenfunctions of Schrödinger operators, and in classical and quantum scattering theory. His most recent research has concentrated on the scattering and spectral theory of quantum particles in homogeneous external fields.

Abel Klein is professor and former chair of the department of mathematics at the University of California, Irvine. He has made fundamental contributions to the theory of random operators, especially to the multiscale analysis, an essential tool on the proofs of spectral and dynamical localization. His most recent work is on transport properties of random operators and characterization of the Anderson metal-insulator transition.

Jean Bellissard of the Georgia Institute of Technology and Institut Universitaire de France is an expert in dissipative processes and transport of quantum particles. Much of his recent work centered on understanding the integer quantum Hall effect and amorphous media. For this task, he and his
co-workers pioneered the use of noncommutative geometry as originated by A. Connes.

H. T.Yau is a professor of mathematics at the Courant Institute of Mathematical Sciences, New York University, and at Stanford University. Yau is a specialist in the application of probabilistic methods to physical problems, such as many-body theory and stability of matter in quantum mechanics, and turbulent fluid flow. He has made deep contributions to probability theory, mathematical physics, and the theory of nonlinear partial differential equations. Much of his work has been concerned with the derivation of transport equations as a time-space limit from a microscopic description (both quantum and classical) and the corresponding fluctuations from this limit. For example, he has been engaged in a series of papers describing how the quantum mechanical description of matter gives rise to the Boltzmann equation that governs the macroscopic behavior of particles. The methods he has developed have had a strong impact on statistical mechanics and the theory of interacting particles. In particular, his relative entropy technique is a standard tool in the field of hydrodynamic limit.

Richard Froese is a professor of mathematics at the University of British Columbia in Vancouver, Canada. With Ira Herbst, he developed the method of positive commutators for the spectral analysis of N-body quantum systems and the analysis of eigen functions. He has been most recently interested in quantization of classical systems, and the spectral and scattering theory of difference operators on graphs. He has studied resonances for quantum systems, and for the Laplace-Beltrami operator on hyperbolic manifolds.

Rafael Benguria is a professor of physics at the Pontificia Universidad Católica de Chile. He has been involved in the fundamental problem of the stability of matter for two decades. He is an expert on estimates for eigenvalues of quantum systems, Lieb-Thirring inequalities, and variational inequalities used in proving lower bounds on the ground state energy. He has been recently involved in the analysis of quantum field theory models.

WEEK TWO: 31 July--4 August 2006

International Workshop on Analysis and Probability in Quantum Physics

The PASI school will be followed by a five-day workshop on Schrodinger operators.

Invited Participants from the Americas

Michael Loss, Georgia Institute of Technology
Eric Carlen, Georgia Institute of Technology
Elliott Lieb, Princeton University
Michael Aizenman, Princeton University
Bruno Nachtergaele, University of California, Davis
Israel Michael Sigal, University of Notre Dame
Laszo Erdos, Georgia Institute of Technology
Mikhail Shubin, Northeastern University
Rafael de Rio Castillo, Universidad Nacional Autonoma de Mexico
Vojkan Jakvsic, McGill University
S. R. S. Varadhan, Courant Institute of the Mathematical Sciences, New York University
Gerard Ben Arous, Courant Institute of the Mathematical Sciences, New York University
Charles Newman, Courant Institute of the Mathematical Sciences, New York University
Jeremy Quastel, University of Toronto
Fraydoun Rezakhanlou, University of California, Berkeley
Gunther Uhlmann, University of Washington
Antonio Sa Barreto, Purdue University
Plamen Stefanov, Purdue University
Carlos Villegas-Blas, Instituto de Matematicas,
Unidad Cuernavaca, Universidad Nacional Autonoma de Mexico, Morelos, Mexico

Invited Participants from other Regions

Shu Nakamura, University of Tokyo
Jean Michel Combes, Université de Toulon et du Var
Dimitri Yafaev, Université de Rennes
Francois Germinet, Université de Cergy-Pontoise
Werner Kirsch, Ruhr Université at Bochum
Vesselin Petkov, Université Bordeaux I
Frederic Klopp, Université Paris XIII
Heinz Siedentop, Universität at Munich
Wolfgang Koning, Technical Universität at Berlin
Herbert Spohn, Universität at Munich
Yves Le Jan, Université Paris Sud

SITE AND FACILITIES

The proposed PASI school and workshop will take place on the San Joaquin campus of the Pontificia Universidad Católica de Chile in Santiago de Chile. Good internet facilities and an outstanding mathematics and physics library will add to the success of the meeting. The campus is conveniently located near the subway station San Joaquin. There are nearby hotels and a student hostel for the PASI program participants.

©2005, Math Department, University of Kentucky, Lexington, KY,
Web contact, Updated: September 6, 2005