Matt Hiking

Matt Holzer
Associate Professor
Department of Mathematical Sciences
George Mason University



Get In Touch:

My office is 4458 Exploratory Hall.

My email is mholzer at gmu.edu.

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:

Fall 2021: Differential Equations (Math 214) and Probability (Math 351)

Spring 2021: Ordinary Differential Equations (Math 677) and Complex Variables (Math 411)

Fall 2020: Partial Differential Equations (Math 678) and Ordinary Differential Equations (Math 214)

Spring 2020: Ordinary Differential Equations (Math 677) and Linear Algebra (Math 203)

Research:

  1. Pattern formation in random networks using graphons, preprint, 2021 (with Jason Bramburger). pdf
  2. Epidemic spreading on complex networks as front propagation into an unstable state, preprint, 2021 (with Ashley Armbruster, Noah Roselli and Lena Underwood). pdf
  3. Asymptotic spreading for Fisher-KPP reaction-diffusion equations with heterogeneous shifting diffusivity. DCDS-S, in press, 2021 (with Grégory Faye and Thomas Giletti). pdf
  4. Locked fronts in a discrete time discrete space population model. submitted, 2020 (with Zachary Richey, Wyatt Rush and Samuel Schmidgall). pdf
  5. Invasion into remnant instability: a case study in front dynamics. to appear in Indiana University Mathematics Journal, 2021 (with Grégory Faye, Arnd Scheel and Lars Siemer). pdf
  6. Asymptotic stability of the critical pulled front in a Lotka-Volterra competition model. Journal of Differential Equations, 269 (9), 6559-6601, 2020 (with Grégory Faye). pdf
  7. Asymptotic stability of the critical Fisher-KPP front using pointwise estimates. ZAMP, 70:13, 2019. (with Grégory Faye). pdf
  8. Estimating epidemic arrival times using linear spreading theory. Chaos, 28(1), 2018 (with Lawrence Chen and Anne Shapiro). pdf
  9. 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
  10. Bifurcation to locked fronts in two component reaction-diffusion equations. Annales de l'Institut Henri Poincaré C, 36(2):545-584, 2019 (with Grégory Faye). pdf .
  11. Invasion fronts on graphs: the Fisher-KPP equation on homogeneous trees and Erdos-Reyni graphs. DCDS-B, 24(2):671-694, 2019. (with Aaron Hoffman). pdf
  12. Linear spreading speeds from nonlinear resonant interaction. Nonlinearity, 30(6):2403-2442, 2017. (with Grégory Faye and Arnd Scheel). pdf
  13. 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
  14. A proof of anomalous invasion speeds in a system of coupled Fisher-KPP equations. DCDS-A, 36(4):2069-2084, 2016. pdf .
  15. 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 .
  16. Criteria for pointwise growth and their role in invasion processes. Journal of Nonlinear Science, 24(4):661-709, 2014. (with Arnd Scheel) pdf .
  17. Anomalous spreading in a system of coupled Fisher-KPP equations. Physica D, 270(1):1-10, 2014. pdf .
  18. Accelerated fronts in a two stage invasion process. SIAM J. Math. Anal. 46(1):397-427, 2014. (with Arnd Scheel) pdf
  19. 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
  20. A slow pushed front in a Lotka-Volterra competition model. Nonlinearity, 25:2151, 2012 (with Arnd Scheel) pdf
  21. 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
  22. 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
  23. 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)
  24. 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)
  25. 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)
  26. 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