10h30: Walking in the Quarter Plane. Manuel Kauers, Risc, Linz, Austria.

We consider certain lattice walks in the plane that are restricted to the first quadrant. Some years ago, Gessel conjectured that the univariate counting function for closed walks (excursions) is holonomic. We will first present a proof of Gessel's conjecture found together with Doron Zeilberger and Christoph Koutschan. In the second part of the talk, we will present the proof of a stronger property, recently discovered together with Alin Bostan: the full (trivariate) Gessel's counting function (for arbitrary walks) is algebraic.