lecturer: Marek Biskup (MS 6617B)
time: MWF 10-11 AM
place: MS 6221
office hours: MWF 1-2

Homework assignments:

Week 1: HW #1 due Wed 4/19/2006;  solutions

Week 4: HW #2 due Fri 5/12/2006; 

Week 6: HW #3 due Wed 5/31/2006; 

Course description: (here's the initial announcement with a wrong classroom number and here are some relevant papers)

This is a topics course on the subject of spin glasses. To explain briefly the name, the word "glass" refers to a disordered material with built-in frustration (which we see when a glass that has survived a fall onto a hard floor, cracks a few months later after coming to a gentle contact with other glasses in the dishwasher), the word "spin" refers to the way the "glass" is modeled -- using spin systems. We will predominantly look at the mean-field version of these systems which are characterized by the fact that every constituent interacts with every other constituent.

The models of spin glasses originated in physics but, recently, developed their cousins in both computer science and optimization theory. As particular examples, we could name the Sherrington-Kirkpatrick model (physics), random k-SAT model (computer science) and random-graph coloring (combinatorial optimization). However, despite their relative simplicity, very little has been known about these models until recently.

In this course I will describe various new approaches to spin-glass systems. I will follow, for the most part, Talagrand's book Spin Glasses: A Challenge for Mathematicians. To complement it with the most recent developments, I will also refer to research papers that are not subsumed by the book (in particular, I plan to present the full proof of Parisi's formula obtained by combination of Guerra's and Talagrand's work). The book is too expensive to buy, but there should be copies on reserve in the library.

Disclaimer: I will be learning the subject along with everybody else in this course. My hope is to reach understanding at the level needed to start doing research in this field. All of you are welcome to join me.

Models to cover:

1. Random-Field Curie-Weiss Model
2. Random Energy Model
3. Sherrington-Kirkpatrick Model
4. Hopfield Model
5. Random-Graph Coloring
6. Random k-SAT

Time-sharing with Tom Liggett's class:

Our course is immediately followed -- same classroom -- by the continuation of Tom Liggett's Interacting Particle System's course. Since both courses will be attended by pretty much the same group of people, we will sometimes take/donate classroom time from/to the other course. Here is how this will be done:

Conditions for getting credit: