My scholarly interests include nonlinear analysis, differential and integral equations, mathematical ecology, fractal geometry, Polanyi’s theory of personal knowledge, and pedagogical tact.
Selected Publications (* denotes HMC student co-author):
- In Praise of Acoustic Mathematics, The Mathematical Intelligencer, to appear 2026
- Radial Solutions to Elliptic Equations, (with A. Castro), Electronic Journal of Differential Equations, Special Issue in Honor of John W Neuberger, (2023), 87-100
- Teaching from the Unknown, Journal of Humanistic Mathematics, Volume 11, Issue 1, January 2021
- Integrodifference models for persistence in temporally varying river environments, (with Y. Jin and M. Lewis), Journal of Mathematical Biology, 70, (2015), 549-590.
- A Boundary Value Problem for integrodifference population models with cyclic kernels, (with T. McAdam*), Discrete Contin Dyn Syst Ser B, 19 (10), (2014), 3191-3207.
- Selling Mathematics: Service & Quality, Journal of Humanistic Mathematics, Volume 3, Issue 2, July 2013
- R₀ Analysis of a Spatiotemporal Model for a Stream Population, (with H. Mckenzie, Y. Jin, and M. Lewis), SIAM Journal on Applied Dynamical Systems, 11 (2) , (2012), 567-596.
- As Flat As Possible, SIAM Review, 49, (2007), 491-507.
- The Liouville-Bratu-Gelfand Problem for Radial Operators, (with K. Schmitt), Journal of Differential Equations, 184, (2002), 283-298.
- Radial Solutions of Quasilinear Elliptic Differential Equations, (with K. Schmitt), Handbook of Differential Equations, (2004), 359-435.
- Traveling Waves and Shocks in a Viscoelastic Generalization of Burgers’ Equation, (with V. Camacho* and R. Guy), SIAM Journal on Applied Mathematics, 68 (5), (2008), 1316-1332.
- Approximations of Continuous Newton’s Method: An Extension of Cayley’s Problem, (with O. Lewis* and B. Tennis*), Electronic Journal of Differential Equations, 15, (2007), 163-173.
- Turing Patterns on Growing Spheres: The Exponential Case, (with J. Gjorgjieva*), Discrete Contin. Dyn. Syst., (2007), Series A, suppl., p. 436-445. Note: There is an error in the diffusion-driven calculation in this paper as kindly pointed out by Madzvamuse et al.: See “Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains, J. Math Biol. (2010)” for an alternate approach to determining the diffusion-driven instability condition.