Focuses on the relationship between definable forcing and descriptive set theory; the forcing serves as a tool for proving independence of inequalities between cardinal invariants of the continuum.

A memoir that studies positive definite functions on convex subsets of finite- or infinite-dimensional vector spaces. It studies representations of convex cones by positive operators on Hilbert spaces. It also studies the interplay between positive definite functions and representations of convex cones.

This work is an account of the results originating in the work of James and the second author in the 1980s relating the representation theory of GL n(F q) over fields of characteristic coprime to q to the representation theory of quantum GL n at roots of unity. The new treatment allows us to extend the theory in several directions. First, we prove a precise functorial connection between the operations of tensor product in quantum GL n and Harish-Chandra induction in finite GL n. This allows us to obtain a version of the recent Morita theorem of Cline, Parshall and Scott valid in addition...

Deals with weighted projective lines, a class of non-commutative curves modelled by Geigle and Lenzing on a graded commutative sheaf theory. They play an important role in representation theory of finite-dimensional algebras; the complexity of the classification of coherent sheaves largely depends on the genus of these curves.

Considers the Restricted, Circular, Planar, Three-Body Problem (RCP3BP) - the problem of studying the planar motions of a small body subject to the gravitational attraction of two primary bodies revolving on circular Keplerian orbits (which are assumed not

Presents generalization of Szemeredi's Regularity Lemma to a certain hypergraph setting.

Considers indecomposable degree $n$ covers of Riemann surfaces with monodromy group an alternating or symmetric group of degree $d$. The authors show that if the cover has five or more branch points then the genus grows rapidly with $n$ unless either $d =