CS 880  Advanced Complexity Theory
Spring 2006 
Course Description
This is an advanced graduate course in complexity theory, bringing you close
to the frontier of current research.
CS 810 provides you with a sound background on the complexity theory from
the 80's and before. CS 880 covers research directions that have been in
vogue more recently.
The Spring 2006 edition of CS 880 focuses on expander graphs and their
applications in complexity theory. After introducing the concept of an
expander and a discussion of the known constructions, we will cover their
use in the design of communication networks, error correcting codes,
derandomization and spaceefficient algorithms for undirected connectivity,
the proof of the PCP Theorem and hardness of approximation results, and
proof complexity.
Time permitting, we will also look at related concepts like extractors.
Text
There is no required text.
Lecture notes will be made available from the course web page.
Prerequisites
Introductory Complexity Theory at the level of CS 810.
Lectures
Currently, three 75minute time slots are reserved for this course,
namely MWF 4:005:15pm. The plan is to have an average of two 75minute
lectures per week. Due to conflicts with faculty candidate talks and
meetings, which slots will be effectively used may change from week to
week. If it works out better, we may end up switching to two different
but fixed time slots.
Also, due to a program committee meeting, the first lecture will
only be on Monday 1/23.
Course Work
 Scribes (20%).
Write lecture notes in groups of two. Someone who missed the class should
be able to learn the material from the notes.
I expect a draft within 24 hours after the lecture, and the final version
a week later.
You need to type your notes in LaTeX using the
guidelines provided.
 Homework (45%).
There will be 3 assignments. You are allowed to discuss the problems in
group but you should write out the solutions on your own.
 Project (35%).
There will be no exams. Instead, you are expected to work out a project
on a topic of your own choosing. The basis should be a recent manuscript or
conference paper on computational complexity, say from 2000 or later.
Although I will suggest some topics during the 5th week of the semester,
I strongly encourage you to start looking for a topic yourself right
away. Suitable places to look for inspiration include the
Electronic Colloquium on
Computational Complexity and the proceedings of
the following conferences: STOC, FOCS, Complexity, ICALP, STACS, Random.
You should discuss your selection with me, and settle down on a
topic before Spring break. You can work in groups of two on
your project but you should first find a topic on your own, and then
look for other people who share your interest. More guidelines will
be posted in due time.
