Marianne Johnson

Marianne Johnson is a Senior Lecturer in the School of Mathematics at the University of Manchester. She is a core member of the tropical mathematics research group and collaborates with institutions including Birmingham, Queen Mary University of London, and Warwick through an LMS Joint Research Network. Her research focuses on algebra and combinatorics, including free Lie algebras, representation theory, semigroup theory, and tropical algebra/geometry. She has contributed to EPSRC-funded projects such as 'Multiplicative Structure of Tropical Matrix Algebra' and 'Modular Lie Powers and Applications,' and participated in the CICADA interdisciplinary project.

Her research interests span a wide array of algebraic topics: free Lie algebras explore the structure of non-associative algebras, while representation theory examines how algebraic structures act on vector spaces. Semigroup theory and tropical algebra involve studying combinatorial and geometric properties of matrices and monoids over semirings. Recent work includes studies on plactic-like monoids, tropical matrix identities, and linear functions preserving Green's relations.

Johnson has co-authored over 29 publications, with recent trends emphasizing tropical algebra's applications to geometric and algorithmic problems, such as tropical matrix groups and hyperplane arrangements. Her work bridges pure mathematics with interdisciplinary fields like computational dynamics and healthcare through collaborations like CICADA. Notable projects include analyzing upper triangular tropical matrices and exploring NP-completeness in gossip monoids.

She has advised three research students and contributed to grants involving EPSRC-funded projects. Her affiliations include the Data Science Institute, Algebra research group, and Tropical Mathematics cluster at Manchester. Her work also intersects with Digital Futures initiatives, reflecting her commitment to advancing computational and theoretical mathematics.