United Kingdom. Career History

structure of the semigroup of n × n tropical matrices and its connection with the geometry of tropical polytopes. • Joint work with Kambites and Izhakian: In [14] we studied the notion of projectivity for tropical semimodules and the related concepts of idempotent and von Neumann regular matrices. We discovered a remarkable connection between von Neumann regular matrices and tropical polytopes of pure dimension. In [13] we studied groups of tropical matrices. We proved that every maximal subgroup of the semigroup of n × n tropical matrices can be identified with the full linear automorphism group of a related tropical polytope. Furthermore, we proved that each such maximal subgroup is isomorphic to a direct product of the real numbers with a finite group. • Joint work with Kambites: In [1] we gave a characterisation of Green’s J-relation, describing the connection between this equivalence relation and various ideas of the rank of a tropical matrix. In [12] we considered the connection between tropical idempotent matrices and finite metric spaces, proving that every n-point metric space can be realised in tropical n-space by the columns of an n × n idempotent matrix with respect to the tropical Hilbert projective metric