Mathematical Physics Seminar

This is the web page for the Mathematical Physics Seminar 2002-2003 at the
Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, Canada.

For inquiries concerning the seminar send email to Jacek Szmigielski, szmigiel@math.usask.ca.


The main focus of the seminar will be the book

Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach

by Percy Deift.

Courant Lecture Notes in Mathematics, Vol. 3, Courant Institute of Mathematical Sciences, New York City, 1999.

Contents:

  1. Riemann-Hilbert Problems
  2. Jacobi Operators
  3. Orthogonal Polynomials
  4. Continued Fractions
  5. Random Matrix Theory
  6. Equilibrium Measures
  7. Asymptotics for Orthogonal Polynomials
  8. Universality

The seminar takes place in McLean Hall 242.1 on Thursdays at 2:30 till 4:00 unless advertised differently.

Next meeting: January 30, 2003 .

Previous meetings: January 23, 2003 , January 16, 2003 , September 18, September 25, October 2, October 9, October 16, October 23 , October 30, November 6, November 13 , November 20, November 27

Forthcoming attractions: February 6 , February 8 Past attractions: October 24, November 1, November 15 .


January 30, 2003

Jacek Szmigielski

Ergodic thery of continued fractions (second part) .


January 23 , 2003

Jacek Szmigielski

Ergodic thery of continued fractions.

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January 16 , 2003

Jacek Szmigielski

Arithmetic continued fractions.

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November 27 , 2002

Hans Lundmark

A Riemann-Hilbert Problem for orthogonal polynomials.

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November 20 , 2002

Hans Lundmark

Chapter 3. Formulas for orthogonal polynomials.

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November 13 , 2002

Hans Lundmark

Finishing chapter 2.

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November 6, 2002

Hans Lundmark

Spectral theory of self-adjoint unbounded operators

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October 30, 2002

Hans Lundmark

On the road again. Limit point/limit circle theory.

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October 23, 2002

Hans Lundmark

Review of some aspects of the theory of self-adjoint extensions of unbounded operators.

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October 16, 2002

Hans Lundmark

Jacobi operators, case of unbounded operators, self-adjoint extensions etc

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October 9, 2002

Hans Lundmark

Jacobi operators, spectral map

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October 2, 2002

Hans Lundmark

Jacobi operators.

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September 25, 2002

Jacek Szmigielski

Riemann-Hilbert problems. Beals-Coifman work on the scattering for the first order systems. Part 2.

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September 18, 2002

Jacek Szmigielski

Riemann-Hilbert problems. Beals-Coifman work on the scattering for the first order systems. Part 1.

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Forthcoming attractions

October 24, 2002

Professor Stanley Gudder, Department of Mathematics University of Denver

Fixed Points of Quantum Operations

McLean Hall , room 142.1
1:00 PM - 2:30 PM

Abstract

Quantum operations frequently occur in quantum measurement theory, quantum probability, quantum computation and quantum information theory. If an operator A is invariant under a quantum operation A fixed point. Physically, the fixed points are the operators that are not disturbed by the action of the quantum operation. Our main purpose is to answer the following question.

If A is a fixed point, is A compatible with the operation elements of the quantum operation?

We shall show in general that the answer is no and we shall give some sufficient conditions under which the answer is yes. Our results will follow from some general theorems concerning completely positive maps and injectivity of operator systems and von Neumann algebras.

This is a report on some recent work that I have done in collaboration with Alvaro Arias and Aurelian Gheondea.

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November 1, 2002

Professor Peter Gibson , Department of Mathematics and Statistics University of Calgary,

Topology and discrete geometry arising from a simple mechanical model

ARTS, room 206
4:00 PM - 5:00 PM

Abstract

In this talk I will explain how inverse problems based on a very simple, discrete, mechanical model lead naturally to some interesting topology and discrete geometry. The mechanical model consists of the linearized dynamics of a chain of oscillators. In analyzing ill-posed inverse problems for such a model, the discrete geometry of a special class of convex polytopes, the so-called permutohedra, comes into play. More precisely, the combinatorics of permutohedra makes it possible to analyze the topological structure of solution sets to the inverse problems.

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November 15, 2002

Professor David C. Brydges, Canada Research Chair Department of Mathematics The University of British Columbia Vancouver, BC Canada and Department of Mathematics University of Virginia Charlottesville, USA

Branched Polymers and Dimensional Reduction

ARTS, room 206
4:00 PM - 5:00 PM

Abstract

The problem of determining the expected end-to-end distance of a long self-avoiding random walk in three dimensions is old and unsolved. Thinking of self-avoiding walk as a model for a long chain molecule makes it natural to generalise the question to other topologies, such as self-avoiding trees. Curiously this problem has a version which is exactly solvable. This exact solution will be the subject of the colloquium. It is based on a paper posted in preliminary form at http://xxx.lanl.gov/abs/math-ph/0107005. I shall make every effort to make the colloquium accessible to a general audience.

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February 6, 2003

Professor Lance Littlejohn, Department of Mathematics and Statistics Utah State University,

The BKS(N,M) Problem in Orthogonal Polynomials

McLean Hall 242.1
2:30 PM - 4:00 PM

Abstract

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February 8, 2003

Professor Lance Littlejohn, Department of Mathematics and Statistics Utah State University,

The Glazman-Krein-Naimark Theorem with Applications

McLean Hall 242.1
2:00 PM - 3:00 PM

Abstract

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