Thursday, December 7, 2017, from 4 to 5:30pm
East Hall, room 3096
Speaker: David J. Fernández Bretón (University of Michigan)
Title: More Ramsey-theoretic statements: uncountably many colours, finite monochromatic sets
Hindman’s theorem states that for every colouring of an infinite abelian group with finitely many colours, there will be an infinite set whose finite sums are monochromatic. Increasing the number of colours to infinitely many makes the theorem fail, as does keeping the number of colours finite but requiring an uncountable monochromatic finite-sum set. Recently Komjáth discovered, however, that by increasing the number of colours to be infinite (even uncountable), and at the same time decreasing the size of our desired monochromatic set to a finite number, it is possible to obtain some positive Ramsey-theoretic results. In this talk I will discuss some of these results, as well as some improvements and generalizations of them that I found over the summer, jointly with my REU student Sung-Hyup Lee.