Jonathan Lopez
PhD
Clinical Associate Professor
Research Topics
Algebraic topology, group theory, and Lie algebras, especially Lie algebras associated to congruence subgroups and cohomology of congruence subgroups; linearity of groups; digital topology; using graph theory to understand algebraic and geometric properties of linear operators.
Selected Publications
- A Differential in the LHS Spectral Sequence for Central Extensions of Quotients of Congruence Subgroups, submitted to the New York Journal of Mathematics, currently under review.
- A classification of small operators using graph theory (with T. Bisson), to appear in São Paulo Journal of Mathematical Sciences.
- A Filtration of GLn(R) by Congruence Subgroups and the Associated Lie Algebra, in progress.
- 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 SLn(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).