# Jerusalem Mathematics Colloquium

Thursday, 20th May 2004, 4:00 pm

Mathematics Building, Lecture Hall 2

The Jerusalem Mathematics Colloquium is happy to host

the first of the three ERDOS LECTURES.

##

Professor Janos Pach

(New York University)

"Forbidden patterns and distances"

** Abstract: **
In 1946, in a paper published in the American Mathematical
Monthly, Erdos raised the following innocent looking question: At
most how many times can a given distance occur among n points
in the plane?

This and many similar geometric and number-theoretic
questions have motivated a lot of research in extremal graph and
hypergraph theory and have led to discovery of several important
combinatorial tools. Nevertheless, we are still far from having a
satisfactory answer to Erdos's original question. All known
approaches to this problem are based on forbidden pattern
arguments.

We outline some old and new ideas leading to the best
known bound of O(n^{4/3}), and discuss whether such arguments can
ever lead to the truth.

Light refreshments will be served at 3:30.

List of talks, 2003-04

List of talks, 2002-03

List of talks, 2001-02

List of talks, 2000-01

List of talks, 1998-99

List of talks, 1997-98