{TALK 
        {"April 9}
        {"Norm-graphs and multicolor Ramsey numbers}
        {"Tibor Szabo}
        {"University of Illinois at Urbana-Champaign}
        {"tszabo@math.uiuc.edu}
        {"Determining the maximum number of edges an $n$-vertex simple graph can have    
when it does NOT contain a fixed subgraph $H$ is one of the oldest and
most-studied problems of Extremal Graph Theory.  The value is called the
{\it Tur\'an number} $ex(n;H)$.  {\it Norm-graphs} were introduced in a paper
by Koll\'ar, R\'onyai and the speaker to answer this question when $H$ is a
complete bipartite graph with appropriate part-sizes.

In this talk we define norm-graphs and discuss some variations
and generalizations of them.  We obtain new sharp bounds for the
Tur\'an number of complete bipartite graphs. Applications in
Discrepancy Theory and Ramsey Theory will also be presented.

This talk presents joint work with Noga Alon and Lajos R\'onyai.
}
}