Recent advances in the study of automorphism groups within graph theory have yielded significant theoretical and applied insights. At its core, the interplay between the algebraic structure of groups ...

Deep in the heart of Microsoft, Jennifer Chayes and Christian Borgs lead a who's who of mathematics and computer science. The goal? To explore anything they please Every weekday afternoon some 20 ...

Commuting graphs have emerged as a powerful framework for elucidating complex relationships within finite group theory. In these graphs, vertices typically represent non-central elements of a group, ...

Graph theory isn’t enough. The mathematical language for talking about connections, which usually depends on networks—vertices (dots) and edges (lines connecting them)—has been an invaluable way to ...

Using “refreshingly old” tools, mathematicians resolved a 50-year-old conjecture about how to categorize important functions called modular forms, with consequences for number theory and theoretical ...