# MathCS Seminar

Title: Upper tails for arithmetic progressions in random sets
Seminar: Combinatorics
Speaker: Lutz Warnke of The University of Cambridge
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2015-11-13 at 4:00PM
Venue: W303
Abstract:
We study the upper tail {\mathbb P}(X \ge (1+\varepsilon) {\mathbb E} X) of the number of arithmetic progressions of a given length in a random subset of [n]=\{1, \ldots, n\}, establishing exponential bounds for which are best possible up to constant factors in the exponent (improving results of Janson and Ruci{\'n}ski). The proof also extends to Schur triples, and, more generally, to the number of edges in random induced subhypergraphs of `almost linear' k-uniform hypergraphs.