Simon Fraser University

Recently, Sherry et al. (2024) reconsidered the pioneering work of Dahlquist and Jeltsch (1979) on circle-contractivity for the study of neural networks. This theory can be used to analyse and improve the robustness of architectures that are devised...

TBA

Shape analysis is a framework for treating complex data and obtain metrics on spaces of data. Examples are spaces of unparametrized curves, time-signals, surfaces and images. In this talk we discuss structure preservation and deep learning for...

We consider neural networks (NN) as discretizations of continuous dynamical systems. There are two relevant systems: the NN architecture on one side and the gradient flow for optimizing the parameters on the other. In both cases, stability properties...

The Simplex method for solving linear programs (LPs) is one of the most widely used LP solvers due to the fact that it runs very quickly in practice. However, despite its practical efficiency and decades of study, it remains unknown whether or not it...

The classical McKay correspondence shows that there is a bijection between irreducible representations of finite subgroups GG of S L ( 2 , C )SL(2,C) and the exceptional divisors of the minimal resolution of the singularity C 2 / GC2/G. This is a...

Distances between the roots of a fixed polynomial appear organically in many places in number theory. For any $f(x) \in \mathbb{Z}[x]$, let $\operatorname{sep}(f)$ denote the minimum distance between distinct roots of $f(x)$. Mahler initiated the...

Varieties that fail to have rational points despite having local points for each prime are said to fail the Hasse principle. A systematic tool accounting for these failures uses the Brauer group to define an obstruction set known as the Brauer-Manin...

Despite extensive research, it is not known whether Oort's conjecture about the existence of supersingular curves is true or false. In the first part of the talk, I will describe supersingular curves and discuss the status of Oort's conjecture (both...

In function approximation, it is standard to assume the availability of an orthonormal basis for computations, ensuring that numerical errors are negligible. However, this assumption is often unmet in practice. For instance, multivariate...