time: MW 2-4 PM
place: Boelter 5514
lecturer: Marek Biskup (MS 6617B)
office hours: WALK IN
Final exam: (due Thursday 3/3/2005 at 3 PM)
Homework assignments:
Course outline: Who is the Ising model named after?
Let's start with the course announcement.
Brief description: The goal of this course is to study the mathematical aspects of the Ising model. This system has been one of the most studied models of theoretical physics; tens of thousands of papers have been written on the subject. What is important for us is that this system exhibits a phenomenon of phase transitions that we know from real life: Magnets normally stick to a metal board; but if you heat them up to a sufficiently high temperature (over the so-called Curie point), they lose their magnetism. We will develop the mathematical framework needed for the formulation of these problems and answer many interesting questions that will come up in our discussions.
What is there to learn: First, you will be able to learn the physical background of statistical mechanics and some lingo surrounding the notions of phase transitions and critical behavior. Second, you will learn how these subjects are properly handled mathematically. Third, you will have a chance to learn a host of techniques that were developed in the last 20-30 years to prove various facts about this (and other) system(s). Finally, we may even get to the questions on the current research front and so you will learn where the whole subject is right now, right here. All in all, the course should be ideal for graduate students who (wish to) work in probability, mathematical physics, solid state physics and/or computer science and would like to receive a broad overview of this area of research.
Prerequisites:
The course prerequisites include sound knowledge of undergraduate probability and analysis; familiarity with the content of MATH 245's, 246's and/or 275's is welcome but not strictly required. Further mathematical tools and techniques will be introduced as needed so come with your mind open to learn new things.
Conditions for getting credit:
Homework will be assigned weekly; the course will finish with an (easy) final examination.