Speaker: Julia Wolf (Forder lecturer) Affiliation: University of Cambridge Time: 15:00 Tuesday, 10 March, 2020 Location: 303-G14 |
It is well known (and a result of Goodman) that a random 2-colouring of the edges of the complete graph K_n contains asymptotically the minimum number of monochromatic triangles (K_3s). Erdos conjectured that this was also true of monochromatic copies of K_4, but his conjecture was disproved by Thomason in 1989. The question of determining for which small graphs Goodman's result holds true remains wide open. In this talk we explore an arithmetic analogue of this question: what can be said about the number of monochromatic additive configurations in 2-colourings of finite abelian groups? The techniques used to address this question, which include additive combinatorics and quadratic Fourier analysis, originate in quantitative approaches to Szemeredi's theorem. This is joint work with Alex Saad (University of Oxford). |