Scientific

I will present recent results from my group that pertain to spatio-temporal patterns formed by social foragers. Starting from work on chemotaxis by Lee A. Segel (who was my PhD thesis supervisor), I will discuss why simple taxis of foragers and randomly moving prey cannot lead to spontaneous emergence of patchiness. I will then show how a population of foragers with two types of behaviours can do so. I will discuss conditions under which one or another of these behaviours leads to a winning strategy in the sense of greatest food intake. This problem was motivated by social foraging in eiderducks overwintering in the Belcher Islands, studied by Joel Heath. The project is joint with post-doctoral fellows, Nessy Tania, Ben Vanderlei, and Joel Heath.

This talk was one of the IGTC Student Presentations.

Doodling has many mathematical aspects: patterns, shapes, numbers, and more. Not surprisingly, there is often some sophisticated and fun mathematics buried inside common doodles. I'll begin by doodling, and see where it takes us. It looks like play, but it reflects what mathematics is really about: finding patterns in nature, explaining them, and extending them. By the end, we'll have seen some important notions in geometry, topology, physics, and elsewhere; some fundamental ideas guiding the development of mathematics over the course of the last century; and ongoing work continuing today.

This talk was one of the IGTC Student Presentations.

In many applications of optimization, an exact solution is less useful than a simple, well structured approximate solution. An example is found in compressed sensing, where we prefer a sparse signal (e.g. containing few frequencies) that matches the observations well to a more complex signal that matches the observations even more closely. The need for simple, approximate solutions has a profound effect on the way that optimization problems are formulated and solved. Regularization terms can be introduced into the formulation to induce the desired structure, but such terms are often non-smooth and thus may complicate the algorithms. On the other hand, an algorithm that is too slow for finding exact solutions may become competitive and even superior when we need only an approximate solution. In this talk we outline the range of applications of sparse optimization, then sketch some techniques for formulating and solving such problems, with a particular focus on applications such as compressed sensing and data analysis.