Georgia Institute of Technology College of Sciences

In my talk I will give a survey on the rise and early development of Extremal Graph Theory, one of the large areas in Discrete Mathematics.I will give a description of the asymptotic solution of extremal graph problems for ordinary graphs, describe the stability method and expose the difficulties connected to hypergraph extremal problems.I will expose several unsolved problems in the field, and move on to some new results.I will also describe the connection of the field to several other areas of Discrete Mathematics, like to Ramsey Theory,Random graphs, Regularity lemma, Quasi-randomness, etc.I will also mention some applications of extremal graph theory. The lecture will be a non-technical one.***Refreshments at 4PM in Skiles 236.***