Tutte Colloquium - Luke Postle

Title: Bridging the gap between Linear and Integer Programming

Abstract: A central open question in extremal design theory is Nash-Williams’ Conjecture from 1970, namely that every triangle-divisible graph on n vertices (for n large enough) with minimum degree at least 0.75n has a triangle decomposition. In this talk, we discuss the history of the problem and our recent resolution of this conjecture, as well as other applications in design theory. We also overview the proof, highlighting the new techniques we developed to resolve the fractional version as well as the full conjecture. Joint work with Michelle Delcourt.