Tuesday, Nov 23, 3:30pm ET (8:30pm GMT, 9:30am Wed NZDT)
Tom Kelly, University of Birmingham
Coloring hypergraphs of small codegree, and a proof of the Erdős–Faber–Lovász conjecture

Abstract:

The theory of edge-coloring hypergraphs has a rich history with important connections and application to other areas of combinatorics e.g. design theory and combinatorial geometry. A long-standing problem in the field is the Erdős–Faber–Lovász conjecture (posed in 1972), which states that the chromatic index of any linear hypergraph on $n$ vertices is at most $n$. In joint work with Dong Yeap Kang, Daniela Kühn, Abhishek Methuku, and Deryk Osthus, we proved this conjecture for every sufficiently large $n$. Recently, we also solved a related problem of Erdős from 1977 on the chromatic index of hypergraphs of small codegree. In this talk, I will survey the history behind these results and discuss some aspects of the proofs.