# Jon Harrison, Ph.D.

Associate Professor of Mathematics

## Education

Ph.D. in Mathematics, University of Bristol, 2001

## Biography

Dr. Harrison joined the Baylor faculty in 2007. Prior to coming to Baylor served as a post-doctoral researcher at the Universität Ulm in Germany (2001-2004) and Visiting Assistant Professor at Texas A&M University (2004-2007). He is a graduate of Bristol University in the United Kingdom and is originally from Cranleigh, UK, the birth place of the famous Cambridge mathematician G.H. Hardy. To date Dr. Harrison has supervised two Ph.D. students

## Research

Dr. Harrison's research is in mathematical physics. He is particularly interested in quantum mechanics on graphs and quantum chaos. Topics of particular interest include anyons on graphs, zeta functions of graphs, the Dirac operator and dynamical calculations of spectral statistics.

## Selected Publications

*Complete dynamical evaluation of the characteristic polynomial of binary quantum graphs, *J.M. Harrison and T. Hudgins, J. Phys. A (2022) https://doi.org/10.1088/1751-8121/ac95e1 arXiv:2101.00006

*Periodic-orbit evaluation of a spectral statistic of quantum graphs without the semiclassical limit, *J.M. Harrison and T. Hudgins, EPL 138 (2022) 30002 arXiv:2101.00006

*Lyndon word decompositions and pseudo orbits on q-nary graphs,* R. Band, J.M. Harrison and M. Sepanski, J. Math. Anal. Appl. 470 (2019) 135-144 arXiv:1610.03808

*n-particle quantum statistics on graphs,* J.M. Harrison, J.P. Keating, J.M. Robbins and A. Sawicki, Commun. Math. Phys. **33** (2014) 1293-1326 arXiv:1304.5781

*Finite pseudo orbit expansions for spectral quantities of quantum graphs, *R. Band, J.M. Harrison and C.H. Joyner, J. Phys. A: Math. Theor. 45 (2012) 325204 arXiv:1205.4214

*Quantum statistics on graphs,* J.M. Harrison, J.P. Keating and J.M. Robbins, Proc. R. Soc. A (2010) doi:10.1098/rspa.2010.0254 arXiv:1101.1535

*Full counting statistics of chaotic cavities from classical action correlations, *G. Berkolaiko, J.M. Harrison and M. Novaes, J. Phys. A: Math. Theor. 41 (2008) 365102 arXiv:cond-mat/0703803

*On occurrence of spectral edges for periodic operators inside the Brillouin zone,* J.M. Harrison, P. Kuchment, A. Sobolev and B. Winn, J. Phys. A 40 (2007) 7597-7618, arXiv:math-ph/0702035

*Quantum graphs where back-scattering is prohibited, *J.M. Harrison, U. Smilansky and B. Winn, J. Phys. A: Math. Theor. 40 (2007) 14181-14193 arXiv:0708.0839

*Quantum Indistinguishability from General Representations of SU(2n)*, J.M. Harrison and J.M. Robbins, J. Math. Phys. 45 (2004), 1332-1358, arXiv:math-ph/0302037

*The Spin Contribution to the Form Factor of Quantum Graphs*, J. Bolte and J.M. Harrison, J. Phys. A: Math. Gen. 36 (2003), L433-L440, arXiv:nlin.CD/0304046

*Spectral Statistics for the Dirac Operator on Graphs*, J. Bolte and J.M. Harrison, J. Phys. A: Math. Gen. 36 (2003), arXiv:nlin.CD/0210029

## Awards

Simons Foundation Collaboration Grant 354583, “Quantum Statistics of Networks Collaboration,” PI, 2015-2022.

NSF Conference Grant DMS-1838054, “Texas Analysis and Mathematical Physics Symposia,” PI (with B. Simanek), 2018-2019.

NSF Grant DMS 0604859 ``Spectral Properties of Quantum Graphs and Related Systems,'' CoPI (with G. Berkolaiko and B. Winn), 2006-2010.

## Former Ph.D. Students

Victoria Hudgins (Now at the Univeristy of Kansas)

Erica Oldaker (Now at Gordon College)

## Teaching Interests

Dr. Harrison has taught a variety of courses including the calculus and advanced calculus sequences, foundations of mathematics, partial differential equations, linear algebra, and graduate real and complex analysis, graph theory, and nonlinear dynamics and chaos.