Dominic Welsh: his work and influence

TL;DR

This paper reviews the extensive influence of Dominic Welsh in mathematics, highlighting his key contributions across discrete probability, matroids, graphs, computational complexity, and Tutte-Whitney polynomials, emphasizing his role in uniting fields and mentoring.

Contribution

It provides a comprehensive overview of Welsh's work and influence, especially in matroid theory and Tutte-Whitney polynomials, showcasing his interdisciplinary impact.

Findings

Welsh's theorems advanced discrete mathematics.

His expository work fostered mathematical development.

Mentorship shaped future mathematicians.

Abstract

We review the work of Dominic Welsh (1938-2023), tracing his remarkable influence through his theorems, expository writing, students, and interactions. He was particularly adept at bringing different fields together and fostering the development of mathematics and mathematicians. His contributions ranged widely across discrete mathematics over four main career phases: discrete probability, matroids and graphs, computational complexity, and Tutte-Whitney polynomials. We give particular emphasis to his work in matroid theory and Tutte-Whitney polynomials.