Seminario: "On the number of monochromatic solutions to multiplicative equations" - Victor Souza

June 29, 2026 - 10:00 a.m.
Aula Consulenze - Dipartimento di Scienze Matematiche
Politecnico di Torino

"On the number of monochromatic solutions to multiplicative equations"
Victor Souza - Cornell University

Abstract: Given an r-colouring of the interval {2, ..., N}, what is the minimum number of monochromatic solutions of the equation xy = z? For r = 2, we show that there are always asymptotically at least (1/2 sqrt{2}) N^{1/2} log N monochromatic solutions, and that the leading constant is sharp. We also establish a stability version of this result and similar, but weaker, bounds for more colours. Joint work with Lucas Aragão, Jonathan Chapman and Miquel Ortega.