MATH 743, Winter 2004, Spectral theory of Anderson type Hamiltonians

  • INSTRUCTOR: Vojkan Jaksic; office: Burn 1209; phone: 3827; e-mail: [email protected]
  • TIME AND PLACE: Wed, 13:00--15:30, Burn 920.
  • PREREQUSITES: MATH 564 and 565.
  • ABOUT THE COURSE: The goal of this course is to give a self-contained description of some new developments in spectral theory of random Schrodinger operators. It will focus on structural spectral properties which will be discussed in great generality using the tools of probability theory and harmonic analysis. Although the course will deal with state of the art research material , the presentation will be essentially self-contained. The basic facts of harmonic analysis, probability and functional analysis needed for the course will be reviewed. The course is aimed at advanced graduate students.
  • SHORT SYLLABUS : (1) Review of the background material: Measure theory, Harmonic analysis and Borel transforms of measures, Selfadjoint operators and spectral theory, Probability theory. (2) The Anderson type Hamiltonians, definition and basic properties. (3) The rank one and two case. (4) Spectral structure of Anderson type Hamiltonians. (5) Aizenman-Molchanov theory. (6) The Anderson model on Z^d. (7) The Anderson model on the Bethe lattice.
  • GRADING: Your grade will be based on a take home final exam.
  • SUPPLEMENTAL: There will be a supplemental exam, counting 100% of the supplemental grade. No additional work will be accepted for D, F, or J.
  • By the direction of Senate (January 29, 2003), all course outlines have to include the following statement: McGill University values academic integrity. Therefore, all students must understand the meaning and consequences of cheating, plagiarism and other academic offences under the Code of Student Conduct and Disciplinary Procedures (see www.mcgill.ca/integrity for more information).
  • NOTES:
  • Lecture1
  • Lecture2
  • Lecture3
  • Lecture4
  • Lecture5
  • Lecture6
    Special lecture by Stanislav Molchanov, March 10, 1-3 pm.
    Title: Topics from 1D localization theory.
    Video of the lecture:
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  • Medium speed (cable, dsl) connection cable.wmv
  • Fast connection (T1 Lan) lan.wmv
  • Mpeg format part1.mpg, part2.mpg
  • Lecture7
  • Lecture8