Montie S. Avery

About Me

I am an NSF Postdoctoral Fellow at Boston University sponsored by Margaret Beck. My research is focused on front dynamics and diffusive stability of coherent structures. I am broadly interested in pattern formation and dynamics of partial differential equations. I received my PhD from the University of Minnesota in June 2022, where my advisor was Arnd Scheel. 

I co-organize the Boston University Dynamical Systems Seminar and the One World Dynamics Seminar. 

Email: msavery@bu.edu

CV (Updated March 2024)

Publications and Preprints

Preprints

• M. Avery. Growth of cancer stem cell-driven tumors: staged invasion, linear determinacy, and the tumor invasion paradox. [preprint]. 

• M. Avery. Front propagation close to the onset of instability. [preprint]

• M. Avery, P. Carter, B. de Rijk, and A. Scheel. Stability of coherent pattern formation through invasion in the FitzHugh-Nagumo system. [preprint]

• M. Avery, M. Holzer, and A. Scheel. Pushed and pulled fronts in a logistic Keller-Segel model with chemorepulsion. [preprint]

Publications

• A. Asch, M. Avery, A. Cortez, and A. Scheel. Slow passage through the Busse balloon --- predicting steps on the Eckhaus staricase. European J. Appl. Math., to appear. [preprint] 

• M. Avery.  Front selection in reaction diffusion systems via diffusive normal forms. Arch. Ration. Mech. Anal. 248 (2024). [preprint]

• M. Avery, M. Holzer, and A. Scheel. Pushed-to-pulled front transitions: continuation, speed scalings, and hidden monotonicity. J. Nonlinear Sci. 33 (2023). [preprint]

• M. Avery and L. Garénaux. Spectral stability of the critical front in the extended Fisher-KPP equation. Z. Angew. Math. Phys. 74 (2023). [preprint]

• M. Avery and A. Scheel. Universal selection of pulled fronts. Comm. Amer. Math. Soc. 2, (2022). 

• M. Avery and A. Scheel. Sharp decay rates for localized perturbations to the critical front in the Ginzburg-Landau equation. J. Dynam. Diffferential Equations (2021). [preprint]

• M. Avery, C. Dedina, A. Smith, and A. Scheel. Instability in large bounded domains --- branched versus unbranched resonances. Nonlinearity 34 (2021). [preprint]

• M. Avery and A. Scheel. Asymptotic stability of critical pulled fronts via resolvent expansions near the essential spectrum. SIAM J. Math. Anal. 53(2) (2021). [pdf]

• M. Avery, R. Goh, O. Goodloe, A. Milewski, and A. Scheel. Growing stripes, with and without wrinkles. SIAM J. Appl. Dyn. Sys. 18(2) (2019). [pdf]

• N. Ankney, M. Avery, T. Khain, and A. Scheel. Pinning and depinning: from periodic to chaotic and random media. Chaos 29 (2019). 

From Undergraduate Research

• U. Abdulla, A. Prinkey, and M. Avery. Evolution of interfaces for the nonlinear double degenerate parabolic equation of turbulent filtration with absorption. II. Fast diffusion case. Preprint: arXiv:1903.08155. 

Some Recent Presentations

Talks

• • Universal spreading into unstable states. Applied Math Seminar, Brown University, December 2023. 

  • Universal selection of pulled fronts. One World Dynamics Seminar, February 2023. Presented as the second part of a two-part talk with Arnd Scheel.

  • Universal dynamics of invasion fronts. Lefschetz Center for Dynamical Systems Seminar, Brown University, November 2022. 

  • Unfolding the transition from pushed to pulled front propagation. Minisymposium: Methods for spectral stability of coherent structures, SIAM Conference on Nonlinear Waves and Coherent Structures, Bremen, Germany, August 2022. 

  • Zigzagging of stripe patterns in growing domains. Minisymposium: Traveling waves: selection principles and stability, SIAM Conference on Analysis of Partial Differential Equations, La Quinta, CA, December 2019. 

  • Pinning and depinning in dynamically generated media. Minisymposium: Recent advances in lattice dynamical systems, SIAM Conference on Applications of Dynamical Systems, Snowbird, UT, May 2019. 

Posters

• Selection principles for fronts invading unstable states. Presented at Drexel Waves Workshop, Drexel University, Philadelphia, PA, March 2023. 

• Growing Stripes, With and Without Wrinkles. Presented at: 

  • Midwest Dynamical Systems Conference, University of Minnesota, Minneapolis, MN, Nov. 2018.

  • KUMUNU Conference on PDE, Dynamical Systems, and Applications, University of Missouri, Columbia, MO, Apr. 2019. 

  • Summer Northwestern Analysis Program, Northwestern University, Evanston, IL, Aug. 2019. 

Teaching

I am currently teaching MA 776 (Partial Differential Equations). The course webpage can be found here. 

Teaching at Boston University

• Fall 2023 - MA 225 (Multivariate Calculus)

Teaching Assistant at University of Minnesota

• Fall 2017 - Math 1271 (Calculus I)

• Spring 2022 - Math 2574H (Honors Linear Algebra and Differential Equations)