### Wednesday, July 15

## IP6

Interaction Between Number Theory and Combinatorics

2:00 PM-3:00 PM

*Chair: Edward R. Scheinerman, Johns Hopkins University *

*Room: Earth Science Center Auditorium *

Number Theory and Graph Theory were not only present but also interwoven in the mathematics of Paul Erdös. The manifestation of this can be seen not only in the methods he introduced and in his proofs but also in the motivation of the questions he asked.

Erdös had already applied graph theory to number theory in 1938 (where the graph results he proved can be considered a forerunner of extremal graph theory). As a continuation, beginning in the 1960s, a wide area has developed where the extremal problems in different structures are the central target of the investigation. The speaker will outline the interaction between number theory and combinatorics, putting the emphasis on extremal problems.

**Vera T. Sós**

*Mathematical Institute of the Hungarian Academy of Sciences*

*Budapest, Hungary*

*MMD, 6/5/98*