Jim Renshaw

Jim Renshaw is an Associate Professor in the Mathematics department at the University of Southampton, where he conducts research in algebraic semigroup theory with particular emphasis on actions of semigroups and monoids on sets and ordered structures.

Renshaw's primary research interests include:

• Algebraic semigroup theory and its applications
• Actions of semigroups and monoids on sets and ordered structures
• Semigroup amalgams and homological classification theory of monoids
• Flat covers and pre-covers of monoid acts
• Structure and actions of E-dense and E-inversive semigroups
• Discrete log problem and its connections with semigroup theory

His publication record shows a clear progression in his research focus, beginning with foundational work on semigroup amalgams and flat covers of monoid acts, then expanding to investigate inverse semigroup actions on graphs and trees, and most recently exploring connections between E-dense semigroups and the discrete log problem. His 2024 paper 'Semilattices of stratified extensions' represents the current direction of his research in ordered algebraic structures.

Renshaw is actively involved in doctoral supervision, currently mentoring William Lee Warhurst who is pursuing an iPhD in Mathematical Sciences. He has indicated that he is accepting applications from prospective PhD students. His teaching interests are concentrated in algebra and number theory, contributing to the mathematics curriculum at the University of Southampton.