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## SMALL SUMSET ALONG A GRAPH

### Antal Balog

Hungarian Academy of Sciences

###
Thursday, May 25, 2006

L01 Carson Hall, 4 pm

Tea 3:30 pm, Math Lounge

**Abstract: ** We walk around the seemingly innocent result,
that if *A* and *B* are finite sets of integers (or vectors
or elements of a torsion free commutative group), *G* is a
"large" subset of pairs *(a,b)* from *A\times B*, but the
sums *a+b:(a,b)\in G* define only a few different elements, then
there are "large" subsets *A'\subset A*, *B'\subset B*
such that ALL of their sums *a+b:a\in A', b\in B'* define only a
few different elements.

The discussion of several applications will
show the importance of this result. We also indicate the main steps of
a simple, elegant, completely elementary proof. No special
prerequisite is needed.

This talk will be accessible to undergraduates.