Lattice Walk Enumeration: Analytic, algebraic and geometric aspects

Abstract: This talk will survey classification of lattice path models via their generating functions.. A very classic object of combinatorics, lattice walks withstand study from a variety of perspectives. Even the simple task of classifying the two dimensional nearest neighbour walks restricted to the first quadrant has brought into play a surprising diversity of techniques from algebra to analysis to geometry. We will consider walks under a few different lenses. We will see how lattice walks can naturally guide the classification of functions into categories like algebraic, D-finite, differentiably algebraic and beyond. Elliptic curves and differential Galois theory play an important role.

algebraic geometrynumber theory

Audience: researchers in the topic

SFU NT-AG seminar

Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

We normally meet in-person in the indicated room. For online editions, we use Zoom and distribute the link through the mailing list. If you wish to be put on the mailing list, please subscribe to ntag-external using lists.sfu.ca