Department of Mathematics and
Statistics
McMaster University
1280 Main Street West
Hamilton, Ontario
Canada L8S 4K1
Teaching Schedule, 20132014 


Course Title  Course Number  Room  Semester 
Time  Course Information  
Algebra I 
MATH 3E03 
HH/305 
Fall 
M, Th, 15:3016:20, Tu 16:3017:20 

Arts&Science Calculus  ARTS&SCI 1D06 
HH/104 
Fall/Winter 
M, W, Th 13:30  14:20 W 9:3010:20 
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Winter Semester Office Hours  
Wednesdays, and Thursdays 14:3015:20 and by appointment 
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.