Arthur B. Coble Memorial Lectures
31st Annual Lecture Series
Noga Alon
Tel Aviv University and Institute for Advanced Study
 will present
Methods in Modern Combinatorics

March 5-7, 2002
A reception will be held in the Colonial Room, Illini Union
5:00 to 6:30 p.m., Wednesday, March 6

Methods in Modern Combinatorics
Combinatorics is an essential component of many mathematical areas, and its study has experienced an impressive growth in recent years. These lectures will discuss two of the main general techniques that played a crucial role in the development of modern combinatorics; algebraic methods and probabilistic methods. Both techniques will be illustrated by examples, where the emphasis is on the basic ideas and the connection to other areas.

Tuesday, March 5, 4:00 p.m., Room 314 Altgeld Hall
1. Dimension, Distances, and Information Theory
Extremal problems in Discrete Mathematics can often be studied by considering the dimensions of appropriately constructed linear spaces. This will be illustrated by several representative examples in Combinatorial Geometry and in Information Theory.
Wednesday, March 6, 4:00 p.m., Room 160 English Building
2. Polynomials, Addition, and Coloring
The lecture will describe a general technique, called "Combinatorial Nullstellensatz", that is based on some simple properties of polynomials. Some of its applications in Additive Number Theory and in Graph Theory will be presented.
Thursday, March 7, 4:00 p.m., Room 314 Altgeld Hall
3. The Probabilistic Method
The discovery that deterministic statements can be proved by probabilistic reasoning led more than fifty years ago to several striking results in Analysis, Number Theory, Combinatorics and Information Theory. It soon became clear that the method, which is now called the probabilistic method, is a very powerful tool for proving results in Discrete Mathematics. The basic approach will be described, focusing on some recent applications as well as on the algorithmic aspects.

 
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