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K-State Today

February 2, 2016

Mathematics Colloquium lecture Feb. 2

By Reta McDermott

Georgios Petridis, University of Rochester, will present, "Two Questions in Arithmetic Combinatorics" as part of the Mathematics Department Colloquium Lecture series at 2:30 p.m. Tuesday, Feb. 2, in 122 Cardwell Hall.

The abstract for the lecture is: Petridis will present two theorems of number-theoretic nature where combinatorial arguments have been particularly effective. Both theorems are related to so-called inverse results of the following kind: Suppose an arithmetic progression satisfies a property P and A is a set of integers which "nearly" satisfies P, then A must "nearly" be an arithmetic progression.

The first concerns cardinality questions on sumsets — or Minkowski sums of sets — in a commutative group. It asserts that if the number of pairwise sums formed by the elements of a set is "small", then so is the set of h-fold sums.

The second concerns exponential sums of finite sets of integers. It says, roughly speaking, that the L^1-norm of the exponential sum of a set with "multidimensional" structure is considerably larger than the minimum. A consequence is that a set whose exponential sum has nearly minimum L^1 norm must be "one-dimensional".