Dr. Lopez is a Western New York native and a Canisius University alumnus. He received a Ph.D. in Mathematics from the University of Rochester in 2010. Dr. Lopez has been teaching locally ever since, and also spent a number of years working as an actuary. He has been teaching at Canisius since Fall 2015.
Dr. Lopez enjoys teaching a wide range of mathematics courses, especially calculus, algebra, and actuarial mathematics. His teaching methods are aimed at helping students develop an appreciation for the usefulness and elegance of mathematics. A special emphasis is placed on getting students to see "the big picture", e.g., to see calculus as the study of how things change.
He likes to get students involved during class in a number of ways, including direct questioning, group work, or problem solving at the board. A fundamental skill that needs to be developed in any mathematics course is the ability to coherently explain the solution to a problem. Many mathematical careers require the explanation of mathematics to non-experts, and Dr. Lopez helps students begin to develop this skill in all of his courses.
Dr. Lopez has a number of research interests, including group theory, Lie algebras associated to congruence subgroups, cohomology of congruence subgroups, linearity of groups, digital topology, and using graph theory to understand algebraic and geometric properties of linear operators.
"A classification of small operators using graph theory" (with T. Bisson), submitted (2017).
"Digital fixed points, approximate fixed points, and universal functions" (with L. Boxer, O. Ege, I. Karaca, and J. Louwsma), Applied General Topology 17 (2), pp. 159-172 (2016).
"Lie algebras and cohomology of congruence subgroups for SL(n,R)", Journal of Pure and Applied Algebra 218 (2), pp. 256-268 (2014).
"Remarks concerning Lubotzky's filtration" (with F. Cohen, M. Condor, and S. Prassidis), Pure and Applied Mathematics Quarterly 8 (1), pp. 79-106 (2012).
"On Lie algebras and cohomology associated to congruence subgroups", Ph.D. Thesis, University of Rochester (2010).