Linfoot Number Theory Seminar
13th October 2021, 11:00 am – 12:00 pm
Fry Building, 4th Floor Seminar Room
A central pursuit of Arithmetic Ramsey Theory is to understand how large a set of integers can be which lacks solutions to a given system of Diophantine equations. A related question asks which systems always have monochromatic solutions under any finite colouring of the positive integers. Both problems have been thoroughly investigated for linear systems of equations, but much less is known for arbitrary polynomial systems. In this talk, I will discuss recent breakthroughs in this area and how they have made use of interactions between analytic number theory and additive combinatorics. Parts of this talk are joint work Sam Chow.