Algorithmic and Enumerative Combinatorics Summer School 2014 |

### Invited Speakers

- Guillaume Chapuy (Université Paris Diderot, France)
**Some aspects of map enumeration**

Absract: Combinatorial maps are 2-dimensional topological structures that describe the embedding of a graph in a surface. These objects have inexhaustible properties and appear in many areas of mathematics or physics, leading to deep connections between them. In particular they have rich enumerative properties, that have been a subject of active research in the last 50 years. The purpose of these lectures is to give some entry points into this field, by explaining a few classical results of map counting. I will mention both the viewpoint of generating functions and the bijective approach, in the case of the plane and higher topologies.Note: For the lecture notes and some articles relevant for this course go to the speaker's homepage via the link "Algorithmic and Enumerative Combinatorics Summer School" .

- Michael Singer (North Carolina State University, U.S.A.)
**Algebraic and Algorithmic Aspects of Difference Equations**

Abstract: The goal of these lectures is to show how the Galois Theory of Linear Difference Equations allows one to discover algebraic relations among solutions of such equations and leads one to algorithms for determining properties of these solutions. I will begin with a gentle introduction to the theory of linear algebraic groups (those groups that occur as Galois groups) and then present the basic features of the Galois theory and resulting algorithms.Note: For the lecture notes and some articles relevant for this course go to the speaker's homepage via the link "AEC Summer School 2014" .

- Mark Wilson (University of Auckland, New Zealand)
**(A Part Of) Analytic Combinatorics in Several Variables**

Abstract: Multivariate generating functions arise at least as often as univariate ones, but difficulties in their analysis have prevented their full potential being realized. Robin Pemantle and the speaker set out to systematize a part of the theory of asymptotic coefficient extraction from multivariate generating functions. The results of this work (with other coauthors) can be found in the book Analytic Combinatorics in Several Variables, which we see as a complement to the univariate work by Flajolet and Sedgewick. I will present a detailed overview of the material in the book, concentrating on those areas that are different from the univariate case and those areas where new entrants to the field can make (in my opinion) the most progress. I intend to present many examples in addition to general theory.Note: For the lecture notes and some articles relevant for this course go to the speaker's homepage via the link "AEC Summerschool" .