Matt Hiking

Matt Holzer
Assistant Professor
Department of Mathematical Sciences
George Mason University



Applications now accepted for 2017 REU program! flyer

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.

About 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.

Teaching:

Spring 2017: Dynamical Systems

Spring 2017: Calculs III

Fall 2016: Modern Applied Math I

Fall 2016: Linear Algebra

Research:

  1. Bifurcation to locked fronts in two component reaction-diffusion equations. submitted, 2017 (with Grégory Faye). pdf .
  2. Invasion fronts on graphs: the Fisher-KPP equation on homogeneous trees and Erdos-Reyni graphs. submitted, 2016 (with Aaron Hoffman). pdf
  3. Linear spreading speeds from nonlinear resonant interaction. submitted, 2016 (with Grégory Faye and Arnd Scheel). pdf
  4. 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
  5. A proof of anomalous invasion speeds in a system of coupled Fisher-KPP equations. DCDS-A, 36(4):2069-2084, 2016. pdf .
  6. 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 .
  7. Criteria for pointwise growth and their role in invasion processes. Journal of Nonlinear Science, 24(4):661-709, 2014. (with Arnd Scheel) pdf .
  8. Anomalous spreading in a system of coupled Fisher-KPP equations. Physica D, 270(1):1-10, 2014. pdf .
  9. Accelerated fronts in a two stage invasion process. SIAM J. Math. Anal. 46(1):397-427, 2014. (with Arnd Scheel) pdf
  10. 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
  11. A slow pushed front in a Lotka-Volterra competition model. Nonlinearity, 25:2151, 2012 (with Arnd Scheel) pdf
  12. 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
  13. 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) pdf
  14. 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)
  15. 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)
  16. 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)
  17. 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:

  1. 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