Discrete Mathematics

On the Chromatic Number of Graphs and Set Systems

Author: 
András Hajnal
Date: 
Wed, Sep 1, 2004
Location: 
University of Calgary, Calgary, Canada
Conference: 
PIMS Distinguished Chair Lectures
Abstract: 

During this series of lectures, we are talking about infinite graphs and set systems, so this will be infinite combinatorics. This subject was initiated by Paul Erdös in the late 1940’s.

I will try to show in these lectures how it becomes an important part of modern set theory, first serving as a test case for modern tools, but also influencing their developments.

In the first few of the lectures, I will pretend that I am talking about a joint work of István Juhász, Saharon Shelah and myself [23].

The actual highly technical result of this paper that appeared in the Fundamenta in 2000 will only be stated in the second or the third part of these lectures. Meanwhile I will introduce the main concepts and state—--and sometimes prove—--simple results about them.

Notes: 
PDF icon Hajnal.pdf
Class: 
Scientific
Subject: 
Discrete Mathematics
Logic and Foundations

Exponential Sums Over Multiplicative Groups in Fields of Prime Order and Related Combinatorial Problems

Author: 
Sergei Konyagin
Date: 
Thu, Apr 1, 2004
Location: 
University of British Columbia, Vancouver, Canada
Conference: 
PIMS Distinguished Chair Lectures
Abstract: 
Let $p$ be a prime. The main subject of my talks is the estimation of exponential sums over an arbitrary subgroup $G$ of the multiplicative group ${\mathbb Z}^*_p$: $$S(a, G) = \sum_{x\in G} \exp(2\pi iax/p), a \in \mathbb Z_p.$$ These sums have numerous applications in additive problems modulo $p$, pseudo-random generators, coding theory, theory of algebraic curves and other problems.
Notes: 
PDF icon Konyagin_Lectures.pdf
Class: 
Scientific
Subject: 
Discrete Mathematics
Group Theory

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