I read Mathematics at University College London where I also received my Ph.D. in 1973, studying topological descriptive set-theory with Professor C. A. Rogers, FRS . As a graduate student, I was at the same time a regular participant of the Logic Seminar organized by Professor Wilfrid Hodges at Bedford College. I spent my two years as post-doctoral fellow (on a personal SRC Fellowship) at Leicester University collaborating with Professor Roy O. Davies. For many long years I was a constant visitor at the University of Wisconsin, Madison visiting Mary Ellen Rudin and participating in seminars on Logic and General Topology, then my two principal research interests. On joining LSE in 1975 I developed a taste for research in the Social Sciences.
I pursue research in both pure and applied mathematics, the link between the two areas being tools from analysis (in the broad sense).
On the pure side, my work focusses on the interplay between Set theory, General topology (in particular the framework of topological groups), Analysis, and Probability. Recent work here has been concerned with category-measure duality, unification of various strands in the theory of regularly varying functions and functional equations; all of these subjects emerge as inter-related if one uses algebraic tools and adopts a topological viewpoint. One example of the new insights this approach affords is a significant simplification in proving the classical characterization of stable probability laws on the line.
On the applied side my research focusses on the mathematics of the Social sciences in the broad spectrum including Economic theory, Accounting theory (involving especially so-called real-options), Finance, and Game theory. Recent research here has been concerned with optimal voluntary-disclosure theory initially in discrete time and currently in continuous time. The ability to model disclosure theory in continuous-time is a break-through that yielding explicit descriptions of strategic behaviour.