Department of Mathematical Sciences
George Mason University
Get In Touch:
My office is 4458 Exploratory Hall.
My email is mholzer at gmu.edu.
There is a phone in my office (703-993-1463) but email is a better way to reach me.
My research interests are in differential equations, existence and stability of traveling waves and pattern formation. Before coming to Mason, I completed my Ph.D. at Boston University and was a postdoc at the University of Minnesota.
Outside of mathematics, I play ultimate frisbee, hike, and spend time with my lovely wife and son.
Fall 2017: On study leave
Spring 2017: Dynamical Systems
Spring 2017: Calculus III
Fall 2016: Modern Applied Math I
Fall 2016: Linear Algebra
- Asymptotic stability of the critical Fisher-KPP front using pointwise estimates. submitted, 2017 (with Grégory Faye). pdf
- Estimating epidemic arrival times using linear spreading theory. in press, Chaos, 2018 (with Lawrence Chen and Anne Shapiro). pdf
- Pattern formation, traveling fronts and consensus versus fragmentation in a model of opinion dynamics. Physics Letters A, 381(37):3197-3202, 2017 (with Ratna Khatri). pdf
- Bifurcation to locked fronts in two component reaction-diffusion equations. Annales de l'Institut Henri Poincaré C, to appear, 2018 (with Grégory Faye). pdf .
- Invasion fronts on graphs: the Fisher-KPP equation on homogeneous trees and Erdos-Reyni graphs. DCDS-B, in press, 2018. (with Aaron Hoffman). pdf
- Linear spreading speeds from nonlinear resonant interaction. Nonlinearity, 30(6):2403-2442, 2017. (with Grégory Faye and Arnd Scheel). pdf
- Wavetrain solutions of a reaction-diffusion-advection model of mussel-algae interaction. SIAM J. on Applied Dynamical Systems, 16(1):431-478, 2017 (with Nikola Popovic). pdf
- A proof of anomalous invasion speeds in a system of coupled Fisher-KPP equations. DCDS-A, 36(4):2069-2084, 2016. pdf .
- Modulated traveling fronts for a nonlocal Fisher-KPP equation: a dynamical systems approach. Journal of Differential Equations, 258(7):2257-2289, 2015. (with Grégory Faye). pdf .
- Criteria for pointwise growth and their role in invasion processes. Journal of Nonlinear Science, 24(4):661-709, 2014. (with Arnd Scheel) pdf .
- Anomalous spreading in a system of coupled Fisher-KPP equations. Physica D, 270(1):1-10, 2014. pdf .
- Accelerated fronts in a two stage invasion process. SIAM J. Math. Anal. 46(1):397-427, 2014. (with Arnd Scheel) pdf
- An analysis of the renormalization group method for asymptotic
expansions with logarithmic switchback terms. Advances in Differential Equations, 19(3-4):254-282, 2014. (with Tasso Kaper) pdf
- A slow pushed front in a Lotka-Volterra competition model. Nonlinearity, 25:2151, 2012 (with Arnd Scheel) pdf
- Existence and Stability of Traveling Pulses in a Reaction-Diffusion-Mechanics System. Journal of Nonlinear Science, 23:129-177, 2013. (with Arjen Doelman and Tasso Kaper) pdf
Analysis of a renormalization group method and normal form theory for perturbed ordinary differential equations. Physica D, 237, 2008. (with Lee Deville, Tony Harkin, Kreso Josic and Tasso Kaper)
Singular perturbations of $z^n$. Transcendental dynamics and complex analysis, 111--137, London Math. Soc. Lecture Note Ser., 348, Cambridge Univ. Press, Cambridge, 2008. (with Bob Devaney, Dan Look, Monica Moreno Rocha and David Uminsky)
Blowup points and baby Mandelbrot sets for singularly perturbed rational maps. Complex dynamics, 51--62, Contemp. Math., 396, Amer. Math. Soc., Providence, RI, 2006. (with Bob Devaney and David Uminsky)
Phase locking in integrate-and-fire models with refractory periods and modulation. Journal of Mathematical Biology 49 (2004), no. 6, 577--603. (with Tomas Gedeon)
Attractor reconstruction from interspike intervals is incomplete. Physica D 178 (2003), no. 3-4, 149--172. (with Tomas Gedeon and Mark Pernarowski)
Undergraduate Research Mentored:
- Invasion fronts and pattern formation in a model of chemotaxis in one and two dimensions. SIAM Undergraduate Research Online. 6 (2013), 228-245. (Koushiki Bose, Tyler Cox, Stefano Silvestri and Patrick Varin) pdf