Quasi-subtractive varieties: a unified framework for substructural, modal and quantum logic. An algebraic theory is proposed that provides a common umbrella for a plethora of non-classical logics. At the same time, it identifies a core that these logics share with classical algebras.
Structure of relations: algebra and applications. Relations and relational structures form the fundamental mathematical essence required for studying computational problems and computational systems. This project will provide new algebraic methods for solving old problems in the theory of relations, informing our understanding of computational complexity and the nature of computing.
Algebraic categories and categorical algebra. Algebra is the study of operations, such as addition and multiplication, and the relationships between these operations. This project will study two exciting new branches of algebra, quantum algebra and postmodern algebra, which will lead to important advances in physics, geometry, and computing.