Philip Holdridge

University of Warwick


Partition Regularity and Piatetski-Shapiro


Linfoot Number Theory Seminar


5th February 2025, 11:00 am – 12:00 pm
Fry Building, 2.04


A common problem in Additive combinatorics is to show that a Diophantine equation has a solution is partition regular, that is, that for every partition of the natural numbers into finitely many sets, there is one such set in which the equation has a solution. One may also look at partitions of certain subsets of the natural numbers, such as the primes. In this talk, I will discuss the problem of showing partition regularity of linear equations in the set of Piatetski-Shapiro numbers, which are numbers of the form floor(n^c) for a fixed parameter c. We will also give an introduction to the transference principle, a method which uses Fourier analysis to "transfer" solutions from a set of positive density in the integers to solutions in a sparse set of integers. This is based on joint work with Sam Chow and Jon Chapman.





Organisers: Holly Green, Besfort Shala

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