Pure Math Grad Colloquium

Xingchi Ruan, Department of Pure Mathematics, University of Waterloo

"Lower bounds on solubility of Diophantine systems"

Given a system of r homogeneous polynomial equations with degree d with rational coefficients, we study the number of variables it needs to possess a non-trivial p-adic solution. We focus on the lower bound of this number. We learn the history and prototype of the problem, as well as the most precise estimation of the lower bound so far.