Welcome to the homepage of Dr James Hook

IMI Prize Fellow at the University of Bath, UK.

JLHinPila.
Enjoying the sun in Pila, Italy.




Research: My work sits at the intersection of Tropical Mathematics, Numerical Linear Algebra, Dynamical Systems, Statistics and Machine Learning. Tropical mathematics was pioneered by the Brazilian mathematician and computer scientist Imre Simon in connection with certain cellular automaton problems in the 1980s. The adjective tropical has been used historically in his honor. The usefulness of tropical mathematics arises from the observations that many mathematical objects that are highly non-linear and therefore intractable to conventional mathematical approaches simplify greatly, even becoming linear when viewed through the lens of tropical mathematics.

Tropical mathematics in general deals with a class of algebraic structures, the canonical example of which is the "max-plus" semiring. Roughly speaking max-plus algebra is the study of equations that are structured around the binary operations of "taking the maximum" and "addition". Tropical mathematics is a fairly young field with enormous potential for applications in practical data analysis problems. Much of the existing theory for tropical mathematics is concerned with pure mathematics questions arising from the study of algebraic geometry and ergodic theory. In my work I exploit and expand the suite of mathematical tools used in these areas to develop exciting new techniques for solving practical data analysis problems, reveling tropical structure in datasets from applications including infrastructure networks, social networks, distributed computing systems and large scale numerical linear algebra problems.

During my fellowship at Bath I aim to advance both the theory and applications of tropical mathematics, in three directions: tropical methods for conventional numerical linear algebra, time series analysis for discrete event systems and network structure analysis via min-plus low rank approximation.




Bio: In 2012 I completed my PhD, titled "Topics in Dynamical Systems", supervised by Professor David Broomhead, at the University of Manchester, UK.

Following my PhD I held a one year EPSRC Doctoral Prize Fellowship, "Smoothing non-smooth systems", at the University of Manchester, with project sponsor Professor Paul Glendining.

From 2013-2016 I was a PDRA with Professor Francoise Tisseur at the University of Manchester on the EPSRC grant EP/I005293 "Nonlinear Eigenvalue Problems: Theory and Numerics".

In 2016 I took up my current post as the Institute for Mathematical Innovation (IMI) Prize Fellow at the University of Bath, UK.