Winter and Summer 2010, Student Research Seminar in Mathematical Physics
NEW: The seminar on March 17 will run 13:00--14:45 and
will be followed by the talk of Robert Seiringer (Princeton/McGill).
Title: "The Critical Temperature of Dilute Bose Gases".
Time/Place: Burnside 920, 15:00--16:00.
NEW: The seminar on March 10 will be given by Stanislav Molchanov
from University of North Carolina.
The title of his lecture is: "On the Idea of Ensemble".
Instructor: Vojkan Jaksic, BURN 1222, 398-3827, jaksic@math.mcgill.ca
Time and Place: Wednesdays, 13:00--15:30, BURN 1234.
Audience: The seminar is addressed to honours undergraduate
students and graduate students who are interested in mathematical physics.
The seminar could be taken for the credit. If you plan to take the seminar for
credit please contact Prof. Jaksic before Dec 20.
Prerequisites: MATH 354 and 355 (could be taken concurrently),
MATH 249 or MATH 366.
Time frame: The seminar will meet once per week for a period of 2-2.5 hours.
The winter part of the seminar will start and end with the winter semester.
The summer part will run June-August.
Summer reserach:
Several research projects and summer research scholarships will be available
to undergraduate students interested in the summer part of the seminar.
The selection will be based on the performance in MATH 354/355 and the winter
part of the seminar. The selection is at the instructor's discretion.
The selected students will be expected to do some independent reading during the month
of May.
Topics to be covered:
Differential Calculus on Banach Spaces.
Frechet derivatives, Taylor expansion, minima and maxima,
Implicit and Inverse Function Theorem.
Applications to Calculus of Variations. The examples to be discussed are
the soap film forming and breaking, Hamilton's principle of least action,
Feynman's path integrals.
Basic limit theorems in probability and applications
to statistical physics.
Law of large numbers, Central Limit Theorem, Large Deviation Principle
(Cramer's Theorem) for i.i.d. random variables. Illustrations of Irreversibility.
Beyond i.i.d.---introduction to ergodic theory. Introduction to
information theory and classical spin systems.
Limit theorems in
non-commutative setting, introduction to quantum information theory and
quantum spin systems.
Self-adjoint operators and spectral theory
Review of Hilbert spaces and operator theory. Compact and trace class operators,
determinants.
Spectral theorem and elements of scattering theory.
Free Bosons and Fermions
Introduction to free quantum field theory, second quantization, Fock spaces.
Statistical mechanics of free bosons and fermions, Bose-Einstein condensation,
non-equilibrium statistical mechanics of quasi-free systems.
Lecture notes:
The lectures notes are typed and edited by Dana Mendelson abd Mireille Prevost.
pdf file
Overview of Probability notes
pdf file
Robert Seiringer's lectures on Bose-Einstein condesation
pdf file
Notes from seminars held in previous years:
Dynamical Systems
pdf file
Notes were taken by Alex Tomberg
Gaussian Random Fields
pdf file
Notes were taken by Alex Tomberg and Vincent Larochelle
Quantum Statistical Mechanics
pdf file
Notes were taken by Ilya Feige and Dana Mendelson.