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Experimental Mathematics Seminar

On Christol's Conjecture

Christoph Koutschan, Johan Radon Institute (RICAM), Linz, Austria

Location:  via ZOOM, link [password: 6564120420 ]
Date & time: Thursday, 22 October 2020 at 5:00PM - 6:00PM

Abstract: Diagonals of rational functions naturally occur in many applications, such as lattice statistical mechanics and enumerative combinatorics. In the mid 1980's Gilles Christol famously conjectured that any globally bounded D-finite function can be expressed as the diagonal of a rational function. We study several families of rational functions in three or four variables and investigate the nature of their diagonals. It is interesting to compare them with the solutions of the telescopers associated to these rational functions. The connection with creative telescoping leads us to eliminate some of the potential counterexamples to Christol's conjecture that were proposed in the literature. This is joint work with Youssef Abdelaziz, Salah Boukraa, and Jean-Marie Maillard.