
Courant Geometry Seminar: Janos Pach
Posted:
Jan 25, 2005 9:53 PM


Geometry Seminar Tuesday October 12 in room 613 WWH at 6:00 P.M
Some Applications of Graph Theory to Geometry
Janos Pach City CollegeCUNY and CIMS
Since the beginnings of extremal graph theory (roughly 50 years) ago, the strength of its new methods has always been best demonstrated by geometric applications. After giving a brief survey of the new techniques, we establish some new results, including the following theorem of Erd"os, Makai and myself. Let $k$ be fixed and $n$ tend to infinity. Then for any set of $n$ points in the plane with minimal distance at least one, and for any $t_1,t_2,...,t_k$, the number of point pairs whose distance is between $t_i$ and $t_i + o(\sqrt{n})$ for some $i$ is at most $\frac{n^2}{2}(1\frac{1}{k+1}+o(1))$.

