# Walks, Difference Equations and Elliptic Curves

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TALK

Prof. Michael Singer (North Carolina State University, USA), 31 October 2017, 2 p.m., RISC seminar room

**Walks, Difference Equations and Elliptic Curves**

In the recent years, the nature of the generating series of the walks in the quarter plane have attracted the attention of many authors. The main questions are: are they algebraic, holonomic (solutions of linear differential equations) or at least differentially algebraic (solutions of algebraic differential equations)?

In this talk, I will review what is known and show how difference Galois theory can be used to decide some of these questions. No previous knowledge of this Galois theory is necessary.

*This is joint work with T. Dreyfus, C. Hardouin and Julien Roques.*