Attention, l'expos� aura lieu au b�timent I, au 1er �tage du Parc Orsay Universit�.

Lattice Walks Restricted to the Positive Quarter Plane (and Octant).

The enumeration of lattice walks in restricted regions is an elegant problem which has recently been the subject of much attention. In this talk, we begin by reviewing previous work on classifying the generating functions of walks with unit steps restricted to the positive quarter plane. The use of 'guess-and-check' methods for determining asymptotics of these walks will also be discussed, followed by the current progress on walks restricted to the positive octant. These new results in three dimensions are obtained by methods which are analogous to those used previously in two dimensions, as well as combinatorial reductions between two and three dimensional walks.