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UID:20260606T050503EDT-1150W2G1RO@132.216.98.100
DTSTAMP:20260606T090503Z
DESCRIPTION:Counting lattice walks confined to cones - Part I\n\nThe study 
 of lattice walks confined to cones is a very lively topic in combinatorics
  and in probability theory\, which has witnessed rich developments in the 
 past 20 years. In a typical problem\, one is given a finite set of allowed
  steps S in Z^d\, and a cone C in R^d. Clearly\, there are |S|^n walks of 
 length n that start from the origin and take their steps in S. But how man
 y of them remain the the cone C?\n	\n	One of the motivations for studying su
 ch questions is that lattice walks are ubiquitous in various mathematical 
 fields\, where they encode important classes of objects: in discrete mathe
 matics (permutations\, trees\, words...)\, in statistical physics (polymer
 s...)\, in probability theory (urns\, branching processes\, systems of que
 ues)\, among other fields.The systematic study of these counting problems 
 started about 20 years ago. Beforehand\, only sporadic cases had been solv
 ed\, with the exception of walks with small steps confined to a Weyl chamb
 er\, for which a general reflection principle had been developed. Since th
 en\, several approaches have been combined to understand how the choice of
  the steps and of the cone influence the nature of the counting sequence a
 (n)\, or of the the associated series A(t)=sum a(n) t^n. For instance\, if
  C is the first quadrant of the plane and S only consists of 'small' steps
 \, it is now understood when A(t) is rational\, algebraic\, or when it sat
 isfies a linear\, or a non-linear\, differential equation. Even in this si
 mple case\, the classification involves tools coming from an attractive va
 riety of fields: algebra on formal power series\, complex analysis\, compu
 ter algebra\, differential Galois theory\, to cite just a few. And much re
 mains to be done\, for other cones and sets of steps.This series of talks 
 given in the framework of the Aisenstadt chair\, will begin with a survey 
 of this topic. The following two talks will deal respectively with proofs 
 of algebraicicty (and D-algebraicity)\, and with recent progresses on walk
 s with arbitrary steps.\n
DTSTART:20181001T200000Z
DTEND:20181001T210000Z
LOCATION:Room 6254\, CA\, Pav. André-Aisenstadt\, 2920\, Chemin de la tour\
 , 5th floor
SUMMARY:Mireille Bousquet-Mélou\, CNRS\, Université de Bordeaux
URL:/mathstat/channels/event/mireille-bousquet-melou-c
 nrs-universite-de-bordeaux-290195
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