Simon Fraser University

A function $f:\F_2^n\to \F_2^n$ is called almost perfect nonlinear (APN) if $f(x) + f(y) + f(z) + f(x + y + z)= 0$ all $x,y,z$ such that $|\{x,y,z,x+y+z\}|=4$.. The motivation to study these functions comes from cryptography, since the defining...

The talk starts with a short survey on a mathematical game known as Racetrack, in which a vehicle moves in discrete rounds and can slightly modify its movement vector every round. The goal is to minimize the amount of rounds needed to attain some...

Results on a two way convection-diffusion problem; an asymptotic error analysis on a piece-wise uniform grid; and a framework for understanding quadrature errors in Finite Element Methods are presented. These results were never published, although I...

The celebrated Erdős-Pósa theorem states that every undirected graph that does not admit a family of k vertex-disjoint cycles contains a feedback vertex set (a set of vertices hitting all cycles in the graph) of size O(k log k). After being known for...

The dimension of a poset P is the minimum number of total orders whose intersection is P. We prove that the dimension of every poset whose comparability graph has maximum degree $\Delta$ is at most $\Delta log^{1+o(1)} \Delta$. This result improves...

Tree structures emerge in various sciences. It is challenging to compare and analyze tree structures as both the size and the number of trees are increasing and there are few tools to describe tree structures in a quantitive, accurate, comprehensive...

The annual Changing the Culture Conference, organized and sponsored by the Pacific Institute for the Mathematical Sciences, brings together mathematicians, mathematics educators and school teachers from all levels to work together towards narrowing...

Decompositions of combinatorial structures translate very often to functional equations with positive coefficients for their generating functions. A theorem by Bender says that if the generating function is univariate and the equation not linear, the...

I will describe a new approach for exhaustively generating combinatorial objects by combining a satisfiability (SAT) solver with an isomorph-free exhaustive generation method such as orderly generation. The SAT solver is able to limit the search to...

Abstract polytopes are a combinatorial generalisation of classical objects that were already studied by the greeks. They consist in posets satisfying some extra axioms. Their rank is roughly speaking the number of layers the poset has. When they have...