Department of Mathematics and
Statistics
McMaster University
1280 Main Street West
Hamilton, Ontario
Canada L8S 4K1
Research Interests: Mathematical logic, universal algebra and computational complexity
I am involved in the study and classification of general algebraic systems. This area of mathematics is often called Universal Algebra and got its start in the 1930s. In order to compare and classify algebras they are often grouped together according to the equations that they satisfy.
Borrowing and expanding on techniques and ideas from mathematical logic,
classical abstract algebra, and also from newer branches of mathematics
such as lattice theory and category theory, powerful tools have been
developed to help organize and understand the structure of varieties
(classes of algebras defined by equations) and the algebras they contain.
Recent advances in the field have opened up a new area of study dealing
with the local structure of finite algebras. This new local theory of
finite algebras has not only been useful in solving several longstanding
problems but it has also suggested a number of new and challenging
research problems.
My current research program involves studying the computational
complexity of subclasses of the Constraint Satisfaction Problem
(CSP). Many well known complexity problems, such as graph
coloring or Boolean satisfiability, can be naturally presented within the
vast CSP framework. Recent work of Bulatov, Jeavons, Krokhin and
others has established a strong connection between the CSP and universal
algebra and some of the important open problems in the field can be
expressed in purely algebraic terms.