Participation to the tutorials is free of additional charge for FOCS
prior registration is required
FOCS registration form).
Tutorials will take place on the
Brown University Campus
in Room 129 in Metcalf Laboratory, at the
Waterman Street and Thayer street (see the
is very close to the Brown
Computer Science department
of Waterman Street and Brook Street).
Participants will be on their own for lunch, with many possibilities
on Thayer street.
A reception will follow from 7-9PM at the conference hotel.
Saturday, October 20, 2007
9:30 - 10:00 Coffee and Snacks
10:00 - 12:00 Tutorial 1 (Chair: Luca Trevisan)
Terence Tao (UCLA)
Structure and Randomness in Combinatorics
Combinatorics, like computer science, often has to deal
with large objects of unspecified (or unusable) structure.
powerful way to deal with such an arbitrary object is to decompose it
into more usable components. In particular, it has proven
to decompose such objects into a structured component, a pseudo-random
component, and a small component (i.e. an error term); in many cases
it is the structured component which then dominates. We
this philosophy in a number of model cases.
1:30 - 3:30 Tutorial 2 (Chair: Daniele Micciancio)
Dan Boneh (Stanford)
A Brief Look at Pairings-Based Cryptography
Over the past few years a new tool from algebraic geometry,
bilinear groups, has transformed public-key cryptography.
groups enable the development of a new generation of cryptosystems
that solve long standing open problems in cryptography and provide
brand new functionality. A few examples include, short digital
signatures, perfect non-interactive zero-knowledge, and efficient
identity-based encryption. In this tutorial we will discuss some
the mathematical tools underlying bilinear groups, including the Weil
pairing and Miller's algorithm. Our focus, however, will be on a
key examples that illustrate how bilinear groups are used to construct
4:00 - 6:00 Tutorial 3 (Chair: Chris Umans)
Daniel Spielman (Yale)
Theory and Applications of Graph
In this lecture, we will study the eigenvalues and eigenvectors
Laplacian and normalized Laplacian matrices of graphs. Our first
will be to provide intution as to why these eigenvectors and
eigenvalues should reveal combinatorial structure. We will
applications of eigenvectors and eigenvalues to drawing, ranking,
partitioning, clustering and coloring problems in graphs. We will
also discuss connections to random walks in graphs, and how they
inspire applications of graph spectra in machine learning and image
segmentation. We will conclude with a discussion of the theory
practice of computing eigenvalues and eigenvectors, and how results
from spectral graph theory may be applied to accelerate those
We will supply examples you can try at home using either Matlab or