Simon Fraser University

The Direct Summand Theorem states that if $R$ is a commutative Noetherian ring, then any finite extension $R\to S$ splits as a map of $R$-modules. This suggests the notion of a splinter as a class of singularities, where we say a scheme $X$ is a...

Conway-Coxeter friezes are arrays of positive integers satisfying a determinantal condition, the so-called diamond rule. Recently, these combinatorial objects have been of considerable interest in representation theory, since they encode cluster...

The Deligne-Mumford compactification, $\overline{M_{0,n}}$, of the moduli space of $n$ distinct ordered points on $\mathbb{P}^1$, has many well understood geometric and topological properties. For example, it is a smooth projective variety over its...

For integers k>=1 and n>=2k+1, the Kneser graph K(n,k) has as vertices all k-element subsets of an n-element ground set, and an edge between any two disjoint sets. It has been conjectured since the 1970s that all Kneser graphs admit a Hamilton cycle...

In the past decade, (artificial) neural networks and machine learning tools have surfaced as game changing technologies across numerous fields, resolving an array of challenging problems. Even for the numerical solution of partial differential...

This is joint work with Uriya First. If $R$ is a ring and $n$ is a natural number, then an Azumaya algebra of degree $n$ on $R$ is an $R$-algebra such that $A$ becomes isomorphic to the $n \times n$ matrix algebra after some faithfully flat extension...

A set of positive integers is called a Diophantine tuple if the product of any two distinct elements in the set is one less than a square. There is a long history and extensive literature on the study of Diophantine tuples and their generalizations...

Classical algorithms are defined on inputs of different sizes. In contrast, data-driven algorithms, that is, algorithms learned from some data, may only be defined on inputs of the same size as the data. What does it mean for an algorithm to be...

In this talk, we study the singularities of secant varieties of smooth projective varieties when the embedding line bundle is sufficiently positive. We give a necessary and sufficient condition for these to have p-Du Bois singularities. In addition...

Derivative-free algorithms seek the minimum of a given function based only on function values queried at appropriate points. Their performance is known to worsen as the problem dimension increases. Recent advances in developing randomized derivative...