UNIVERSITY OF CRETE - DEPARTMENT OF MATHEMATICS
Knossos Ave., GR 714 09 Iraklio, Crete, Greece, Tel: +30 2810393800, Fax: +30 2810393881


ANALYSIS SEMINAR

Talk by Alex Iosevich

INCIDENCE THEORY AND ERDOS-FALCONER DISTANCE PROBLEMS

27 April 2004

Let ${\{b_j\}}_{j=1}^N$ be a convex sequence of real numbers. Let ${\cal N}_d$ denote the number of solutions of the equation

\begin{displaymath}b_{i_1}+\dots+b_{i_d}=b_{j_1}+\dots+b_{j_d}. \end{displaymath}

Much work has been done on this question in number theory in the context of concrete sequneces like $b_j=j^k$. The question we ask is whether one can obtain good bounds on ${\cal N}_d$ using the convexity assumption alone. We shall see that this is possible to a certain degree. We shall also discuss connections between this problem and related problems in geometric combinatrics.


Mihalis Kolountzakis 2004-04-19