University of Victoria

Given positive integers $p,q$ where $p$ is even and $p\geq 2q$, a circular $\frac{p}{q}$-flow in a mono-directed signed graph $(G, \sigma)$ is a pair $(D, f)$ where $D$ is an orientation on $G$ and $f: E(G)\to \mathbb{Z}$ satisfies that for each...

Naively implemented, statistical procedures are prone to leaking information about their training data, which can be problematic if the data is sensitive. Differential privacy, a rigorous notion of data privacy, offers a principled framework to...

The stochastic heat equation (driven space-time white noise) arises from interface growth dynamics via the Kardar-Parisi-Zhang equation and from the theory of disordered systems via continuum directed random polymers. Despite these physical relations...

We prove that a well-known graphical expansion of the Ising model, known as the Loop O(1) model, is a factor of i.i.d. on unimodular random rooted graphs under various boundary conditions and in the presence of a non-negative external field. As an...

I will present new, non-asymptotic bounds on the heights of random combinatorial trees and conditioned Bienaymé trees, as well as stochastic inequalities relating the heights of combinatorial trees with different degree sequences. The tool for most...

One of the challenges of the accurate simulation of turbulent flows is that initial data is often incomplete. Data assimilation circumvents this issue by continually incorporating the observed data into the model. A new approach to data assimilation...

Abstract: I will describe variational problems whose solutions imply statements about dynamical systems, as well as how relaxations of these variational problems often can be solved computationally using tools of polynomial optimization. The talk...

In 1975, the physicists Imry and Ma predicted that the incorporation of a random field in low-dimensional spin systems leads to the rounding of first-order phase transitions. These predictions were rigorously established by Aizenman and Wehr in 1989...

What do thunderstorms look like on the inside? Were they any different 30 to 50 thousand years ago? How might they change in the next 100 years as global temperatures continue to rise? The presentation will start with how a thunderstorm looks in 3-D...

A process Y is a factor of a process X if it can be written as Y=F(X) for some function F which commutes with translations. The factor is finitary if Y_0 is almost surely determined by some finite portion of the input X. Given a process Y, the...