Matthew A. Valeriote
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Professor
HH 323
(905) 525 9140 ext. 23402
(905) 522-0935
...

Research Area: Mathematical Logic

Research Profile: Mathematical logic,universal algebra and computational complexity

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.

Mathematical logic and universal algebra

2017/2018
Math 1A03
Math 1MP3
Math 4GR3

2016/2017
Arts & Science 1D06
Math 3E03

2015/2016
Math 3A03
Math 3E03
Math 4LT3/6LT3

2014/2015
Arts & Science 1D06
Math 3E03

2013/14
Arts & Science 1D06 - Fall, 2013
Arts & Science1D06 - Winter, 2014
M3E03 - Fall, 2013

  1. S. Bova, H. Chen, and M. Valeriote, Generic Expression Hardness Results for Primitive Positive Formula Comparison, Information and Computation, Vol. 222 (2013), 108-120. 
  2. P. Idziak, P. Markovic, R. McKenzie, M. Valeriote, and R. Willard, Tractability and learnability arising from algebras with few subpowers,  SIAM Journal on Computing, Vol. 39 (7) 2010, 3023-3037. 
  3. J. Berman, P. Idziak, P. Markovic, R. McKenzie, M. Valeriote and R. Willard, Varieties with few subalgebras of powers, Transactions of the American Mathematical Society, Vol. 362, Number 3, March 2010, 1445-1473.
  4. R. Freese, M. Valeriote, On the complexity of some Maltsev conditions, International Journal of Algebra and Computation, 19 (2009), no. 2, 451-464. 
  5. P. Idziak, R. McKenzie and M. Valeriote, The structure of locally finite varieties with polynomially many models, the Journal of the American Mathematical Society, 22 (2009), no. 1, 119-165.

Currently Supervising:
Alberto Chicco (PhD Math)
James Rooney (PhD Math)
Michael Verwer (MSc Math)

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McMaster University - Faculty of Science | Math & Stats