Meetings/Workshops on Graph Theory and Combinatorics in Canada

A permutation is an ordering or arrangement of a set of objects. One might think of shuffling a pack of cards, or sorting a list of options into order of preference, or arranging the seating of passengers on an aeroplane or guests at a dinner. Permutations are central objects in many areas of mathematics. This workshop will explore aspects of permutations which arise in probability theory and related fields. This is a highly active area of study, with a variety of striking results in the last few years and many challenging problems outstanding. Random permutations have applications ranging from genetics to comupter science to economics, and arise in many challenging questions throughout mathematics. Many interesting random processes can be thought of as permutations evolving over time. The workshop will bring together researchers from many backgrounds including probability, combinatorics, physics and theoretical computer science, with the goal of advancing our understanding of random permutations and permutation processes, and of sharing ideas from across the many disparate fields where they are studied.

Dynamics is the study of systems that evolve over time. Combinatorics is the study of discrete structures such as binary strings, well-formed expressions in simple languages, data trees, colorings of graphs, etc. In Dynamical Algebraic Combinatorics, we study key parameters associated with these systems as they evolve, which helps us make sense of the underlying dynamics.

Two groups of mathematicians, who specialize either in topological combinatorics or in combinatorial commutative algebra, are organizing a workshop in order to identify and to work on problems in the intersection of both fields. Topological combinatorics uses tools from topology to study discrete structures, while combinatorial commutative algebra also studies discrete structures but uses algebraic tools. As a result, the two groups of mathematicians may be studying the exact same problem about discrete structures, but using completely different tools and mathematical language. As an example, questions about the enumeration of the faces of a topological object called a Cohen--Macaulay flag complex can be translated into questions about Hilbert functions of ideals. The goal of this workshop is to bring together 21 mathematicians in both fields to facilitate discussions and encourage new collaborations between these two groups. The organizers have identified five possible themes that will bring an additional focus to the direction of the workshop.