About Me

I am an NSERC + Simons Postdoctoral Fellow in the Center for Mathematical Biology at the University of Pennsylvania where I am working with Yoichiro Mori. I received my PhD in Applied Mathematics from the University of British Columbia under the supervision of Michael Ward and Juncheng Wei.

Research

I am primarily interested in the analysis of pattern formation in mathematical models of biological systems. Recently I have been using a combination of formal, computational, and rigorous tools to analyze localized patterns in novel reaction-diffusion systems. Specifically I have been analzying the existence and linear stability of localized solutions in reaction-diffusion systems incorporating bulk-surface coupling, boundary inhomogeneities, as well as anomalous diffusion.

1 / 3
Competition instability in a bulk-surface coupled system (see [6] below).
2 / 3
Splitting instability in the 3D Gierer-Meinhardt system (see [4] below).
3 / 3
Boundary layer instability in the 2D Gierer-Meinhardt System (see [1] below).

Publications

  1. Stability of spike solutions to the fractional Gierer-Meinhardt system in a one-dimensional domain
    with J. Wei and W. Yang. Preprint, to appear in Numerical Mathematics: Theory, Methods and Applications (36 pages)
  2. Boundary layer solutions in the Gierer-Meinhardt system with inhomogeneous boundary conditions
    with L. Mei and J. Wei. Physica D: Nonlinear Phenomena (2022). (16 pages)
  3. Pattern forming systems coupling linear bulk diffusion to dynamically active membranes or cells
    with S. Iyaniwura, F. Paquin-Lefebvre, and M. J. Ward. Phil. Trans. R. Soc. A. (2021). (22 pages)
  4. Multi-spike patterns in the Gierer-Meinhardt system with a nonzero activator boundary flux
    with J. Wei. J. Nonlinear Sci. (2021). (41 pages)
  5. An asymptotic analysis of localized three-dimensional spot patterns for the Gierer-Meinhardt model: existence, linear stability, and slow dynamics
    with M.J. Ward and J. Wei. SIAM J. Appl. Math. (2021). (29 pages)
  6. Hopf bifurcations from spike solutions for the weak coupling Gierer-Meinhardt system
    with L. Mei and J. Wei. European Journal of Applied Mathematics (2021). (33 pages)
  7. The linear stability of symmetric spike patterns for a bulk-membrane coupled Gierer-Meinhardt model
    with M.J. Ward and J. Wei. SIAM J. Appl. Dyn. Syst. (2019). (40 pages)
  8. Stable and unstable periodic spiky solutions for the Gray-Scott system and the Schnakenberg system
    with L. Mei and J. Wei. J. Dyn. Diff. Eqns. (2019). (41 pages)
  9. On isospectral deformations of an inhomogeneous string
    with K. Colville and J. Szmigielski. Comm. Math. Physics 348 no. 3 (2016). (12 pages)
  10. Asymptotic analysis of narrow escape problems in nonspherical three-dimensional domains
    with A.F. Cheviakov. Phys. Rev. E. (2015). (12 pages)
  11. The Canada Day Theorem
    with H. Lundmark and J. Szmigielski. Electron. J. Combin. (2013). (16 pages)

Teaching

Current

I am not currently teaching any courses.

Past

  • Fall 2021: MATH 114 (Calculus II) at the University of Pennsylvania
  • Fall 2018: MATH 110 (Differential Calculus) at the University of British Columbia

Contact Me

  • Address

    Office 3N8A
    David Rittenhouse Lab
    209 South 33rd Street
    Philadelphia, PA 19104-6395
  • Email

    d1gomez@sas.upenn.edu