University of Victoria

Single-cell omics data play a pivotal role in identifying cell-to-cell heterogeneity, understanding cell differentiation, unveiling cell population structures, and ultimately deciphering disease pathogenesis. Due to inherent high-dimensionality...

In this talk, I will present a recent work in which two co-authors and myself studied the behaviour of a local algorithm optimizing the weight of a graph. More precisely, the process starts with a given subgraph H of the complete graph with uniform...

Turán-type problems for hypergraphs have been an intriguing area of research. Despite significant efforts, the Turán density of F is known for only a few three-uniform hypergraphs F. This talk concerns Turán-type problems for 3-uniform tight cycles C...

Given graphs $G$ and $H$ and a positive integer $q$, an $(H,q)$-coloring of $G$ is an edge-coloring in which each copy of $H$ receives at least $q$ colors. Erdős and Shelah raised the question of determining the minimum number of colors, $f(G,H,q)$...

We consider a class of disordered mean-field combinatorial optimization problems, focusing on the Gibbs measure, where the inverse temperature does not vary with the size of the graph and the edge weights are sampled from a general distribution. We...

"Double dipping" is the practice of using the same data to fit and validate a model. Problems typically arise when standard statistical procedures are applied in settings involving double dipping. To avoid the challenges surrounding double dipping, a...

For every $k\ge 2$ and $\Delta$, we prove that there exists a constant $C_{\Delta,k}$ such that the following holds. For every graph $H$ with $\chi(H)=k$ and every tree with at least $C_{\Delta,k}|H|$ vertices and maximum degree at most $\Delta$, the...

The line graph of a graph $G$ is the graph $L$ with vertex set $E(G)$ in which two vertices are adjacent if and only if the corresponding edges of $G$ share an endpoint. A famous theorem of Beineke characterizes the class of line graphs by a list of...

Recent advances in single cell sequencing has led to the availability of gene expression data. We model the trajectories of cells in gene expression space using a diffusion and gradient drift process that also undergoes branching. In this talk, we...

In this talk, I will describe some progress towards the construction of the 3D Yang-Mills (YM) measure. In particular, I will introduce a state space of “distributional gauge orbits” which may possibly support the 3D YM measure. Then, I will describe...