Past Events

How do simple local interactions combine to produce complex large-scale structure and patterns? The abelian sandpile model provides a beautiful test case. I'll discuss a pair of conjectures about the scale invariance and dimensional reduction of the...

The "colored Tverberg problem" asks for a smallest size of the color classes in a (d+1)-colored point set C in R^d that forces the existence of an intersecting family of r "rainbow" simplices with disjoint, multicolored vertex sets from C. Using...

In the early 60s Kesten showed that self-avoiding walk in the upper half plane has a decomposition into an i.i.d. sequence of "irreducible bridges". Loosely defined, a bridge is a self-avoiding path that achieves its minimum and maximum heights at...

This SCAIM lecture is more of a tutorial than a talk. I will present a simple Finite Element Method (FEM) code as a model for the more complex codes in common modern use. Code components include: mesh generation, matrix assembly, a linear solver, and...

We show that on a smooth compact Riemann surface with boundary (M_0, g) the Dirichlet-to-Neumann map of the Schr\"odinger operator \Delta_g + V determines uniquely the potential V. This seemingly analytical problem turns out to have connections with...

In the first half of the talk, I will explain the notion of PT stability, as defined by Bayer. I will also explain how it is related to classical stability conditions on sheaves, and other Bridgeland-type stability conditions. In the second half of...

We wish to understand the boundary between forbidden configurations on 4 rows that yield a quadratic bound and those that have cubic constructions. The result is joint with my supervisor and Attila Sali. The bounds we are concerned with are the...

Studies of the biological effect of ionizing radiation on tissues started almost as soon as the x-ray was discovered by Roentgen in 1895. The need for these studies was also motivated by the early adoption of radiation to treat cancers. Great strides...

Let $M(\alpha)$ denote the Mahler measure of the algebraic number $\alpha$. Dubickas and Smyth constructed a modified version $M_1$ of $M$ having the triangle inequality. $M_1$ is called the metric Mahler measure. We produce an entire parametrized...

Starting from a classical result of Skolem, Mahler and Lech for linear recurrence sequences, we present an algebraic geometric generalization of it. Then we interpret our result from the point of view of dynamics, linking it with the Mordell-Lang...