University of Victoria

This talk will present a novel discretization scheme for Wasserstein gradient flows (i.e. curves of steepest descent for functions of probability measures) based on the successive computation of Schrödinger bridges with equal marginals. In doing so...

In defining colouring of oriented graphs via homomorphism one finds an easily checkable necessary condition for a valid colouring — vertices at directed distance at most two must receive different colours. With this idea in mind we extend the...

Many fundamental problems in extremal combinatorics can be expressed as inequalities in graph homomorphism densities. In this talk, I will introduce some new results on this topic. Our research involves Sidorenko's conjecture, Kohayakawa-Nagle-R{\"o...

The classical Peierls argument establishes that percolation on a graph G has a non-trivial (uniformly) percolating phase if G has “not too many small cutsets”. Severo, Tassion, and I have recently proved the converse. Our argument is inspired by an...

A classical question in extremal (hyper)graph theory asks for tight minimum degree conditions which force the existence of certain spanning structures in large graphs, generalising Dirac's theorem from 1952. One aspect of this concerns tiling graphs...

Let $G$ be a graph with $n$ vertices. Let $A(G)$ be its adjacency matrix. Let $\lambda_1(G), \lambda_2(G)$ denote the largest and second largest eigenvalues of the adjacency matrix. Bollob\'{a}s and Nikiforov (2007) conjectured that for any graph $G...

The notions of noise sensitivity and stability were recently extended for the voter model, a well-known and studied interactive particle system. In this model, vertices of a graph have opinions that are updated by uniformly selecting edges. We...

I will present a coupling between a massive planar Gaussian free field (GFF) and a random curve in which the curve can be interpreted as the level of the field. This coupling is constructed by reweighting the law of the standard GFF-SLE_4 coupling. I...

Spin glasses are disordered statistical physics system with both ferromagnetic and anti-ferromagnetic spin interactions. The Gibbs measure belongs to the exponential family with parameters, such as inverse temperature $\beta>0$ and external field $h...

An edge mapping of a graph is a function f:E(G) -> E(G) where f(e) \neq e for all e in E(G). A subgraph H of G is called f-free if for every e in E(H) f(e) \notin E(H). A graph G is called unavoidable for a graph H if every edge mapping of G has at...