Hi All,

Coming up next, we’ll have a talk by Jacob Hicks continuing on the “geometry of numbers” theme. More detailed information below!

Hope to see you there,
-Danny

Title: The Cochrane-Mitchell Theorem

Abstract: We present Cochrane-Mitchell’s strengthening of the GoN proof of Legendre’s Theorem which simultaneously achieves the existence of a solution and the Holzer bound on the size of a solution. The key idea is to choose a “better lattice”: one with congruence
properties modulo 2abc rather than modulo abc. This turns out to use significantly more GoN input, namely the sharp value of the three dimensional Hermite constant and the classification of extremal (a theorem of Gauss). Time permitting, we will discuss a natural followup question: what are the “best lattices” one can find in this context?