Algebraic combinatorics is the study of combinatorial objects as an extension of the study of
finite permutation groups, or, in other words, group theory without groups. In the spirit of …

This is a survey of distance-regular graphs. We present an introduction to distance-regular
graphs for the reader who is unfamiliar with the subject, and then give an overview of some …

Transformers play a central role in the inner workings of large language models. We
develop a mathematical framework for analyzing Transformers based on their interpretation …

Most coding theory experts date the origin of the subject with the 1948 publication of A
Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has …

This survey is mainly intended for non-specialists, though we try to include many recent
developments that may interest the experts as well. We want to study “good” finite subsets of …

This survey discusses recent developments in the context of spherical designs and minimal
energy point configurations on spheres. The recent solution of the long standing problem of …

We propose a homogeneous primal-dual interior-point method to solve sum-of-squares
optimization problems by combining nonsymmetric conic optimization techniques and …

As with classical computers, quantum computers require error-correction schemes to reliably
perform useful large-scale calculations. The nature and frequency of errors depends on the …

Nano-and microscale particles, such as colloids, commonly interact over ranges much
shorter than their diameters, so it is natural to treat them as “sticky,” interacting only when …

We give a rigorous computer-assisted proof that the triangular bipyramid is the unique
configuration of five points on the sphere that globally minimizes the Coulomb (1/r) potential …