Simon Fraser University

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...

We introduce an efficient algorithm, called partition of unity extension or PUX, to construct an extension of desired regularity of a function given on a complex multiply connected domain in $2D$.Function extension plays a fundamental role in...

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 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...

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...

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...

What is a game? Mathematically speaking, a game has players, strategies and scores to explain why the players win or lose. Games which are modelled with differential equations are called differential games. Common examples are pursuit-evasion games...

Compressive sensing has generated tremendous amounts of interest since first being proposed by Emmanuel Candes, David Donoho, Terry Tao, and others a bit more than a decade ago. This mathematical framework has its origins in (i) the observation that...

Neural networks are remarkable families of non-linear functions that form the backbone for state-of-the-art algorithms in tasks from computer vision (self-driving cars), natural language processing (Google Translate) and reinforcement learning...

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...