Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Tuesday, July 03, 2012, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: József Solymosi (University of British Columbia)

On the Sum-Product Problem

Let A be a finite subset of integers. Erdos and Szemeredi conjectured that either the sum set, A+A, or the product set, A*A should be large for any choice of A. More precisely if A+A={a+b| a,b in A} and A*A={ab| a,b in A} then |A+A|+|A*A|>|A|^{2-c} for any c>0 and large enough A. Variants of this problem have important applications to expander graphs, randomness extractors, and detecting almost primes (among other applications) I will talk about the history of this problem and about some recent developments.

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