Past Events

Consider a random uniform sample of size $n$ over a bounded region $A$ in $R^d$, $d \geq 2$, having a smooth boundary. The coverage threshold $T_n$ is the smallest $r$ such that the union $Z$ of Euclidean balls of radius $r$ centred on the sample...

Spatial Pattern Formation and the Evolution of Cooperative Behaviour

Spatial Pattern Formation and the Evolution of Cooperative Behaviour

In 1974, Briançon and Skoda answered a question of Mather, showing that for $I=(f_1,\dots,f_n)$ an ideal of the coordinate ring at a smooth point on a complex algebraic variety, there is a containment $\overline{I^{n+k-1}}\subseteq I^k$ for all $k...

The question of whether one graph can be embedded in another is a fundamental problem in graph theory. In 2020, Joos and Kim introduced a generalization of the basic graph embedding problem to graph collections. Let $G=\{G_1,\ldots,G_m\}$ be a...

We survey some new and old, positive and negative results on a priori estimate, regularity, rigidity, and constant rank results for special Lagrangian and quadratic Hessian equations. These equations originate in calibrated, convex, conformal, and...

I will present the invariance of extremal Kahler manifolds under a suitable class of bimeromorphic morphisms. Focusing mostly on the cscK (constant scalar curvature Kähler) case, I will show how the main result is obtained as a consequence of a...

One of the main goals of statistical mechanics is to understand critical phenomena of lattice models. This can be achieved by computing the so-called critical exponents, which govern algebraic scaling near or at the critical point. This task is...

We built an age- and immunity-stratified COVID-19 model with setting-specific contacts (home, school, workplace, other) and calibrated it to Ontario’s pre-Omicron incidence and hospital admissions. Counterfactuals toggled vaccination and varied NPIs...

The Laplacian matrix L of a signed graph G may or may not be invertible. We present an entrywise combinatorial formula for the Moore-Penrose inverse of L, obtained by deriving a combinatorial expression for the Moore-Penrose inverse of an incidence...