People

Department of Mathematics Directory

  • Dominic Felix Blanco
  • Dominic Felix Blanco
  • Hill Assistant Professor
  • Postdoc
  • Faculty
  • Partial Differential Equations
  • Specialty Area: Computer-Assisted Proofs for PDEs in Pattern Forming Systems
  • office: Hill 546
  • Office Hours Custom:

    252: Mondays, 11:00 am - 12:20 pm

    244: Mondays, 12:30 pm - 1:50 pm
  • Campus: Busch
  • Research Interests: Computer-Assisted Proofs, Validated Numerics, Pattern Formation, PDEs
  • Bio:

    I received my Ph.D. from McGill University in Montreal, Quebec in 2026 under the supervision of Dr. Jean-Philippe Lessard. My research primarily concerned computer-assisted proofs and validated numerics for PDEs in pattern forming systems.

     

    I began my undergraduate studies at St. Petersburg College (SPC) in St. Petersburg, Florida as part of the dual enrollment program. I received my associates degree from SPC in 2019. Following this, I attended the Wilkes Honors College(WHC)  at Florida Atlantic University (FAU) in Jupiter, Florida. Here, I studied mathematics, physics, and economics receiving bachelors degrees with concentrations in all three in 2022. While completing my undergraduate studies at the WHC, I began taking graduate mathematics courses at the main campus in Boca Raton, Florida. After one additional semester, I received my masters degree in mathematics from FAU. My thesis was supervised by Dr. Jason Mireles-James. Following this, I went to McGill University in Montreal, Quebec to work with Dr. Jean-Philippe Lessard. My research focused on PDEs posed on unboudned domains, which I applied to problems in pattern formation.  I now focus on these problems in this field which can be approached using computer-assisted proofs and validated numerical methods.
  • Publications:

    1.) M. Cadiot and D. Blanco. Localized stationary patterns in the 2D Gray Scott model: computer-assisted proofs of existence. Nonlinearity, 38(4):045016, 2025.

    2.)  D. Blanco and M. Cadiot. Proving Symmetry of Localized Solutions and Application to Dihedral Patterns in the Planar Swift–Hohenberg PDE. SIAM Journal on Applied Dynamical Systems, 25(3):1759–1807, 2026.

    3.) D. Blanco. Proving the existence of localized patterns, periodic solutions, and branches of periodic solutions in the 1D Thomas model. Mathematics and Computers in Simulation 251, 198-232, 2027.

    Submitted pre-prints:

    4.) D. Blanco, M. Cadiot, and D. Fassler. Proving the existence of localized patterns and saddle node bifurcations in 1D activator-inhibitor type models. arXiv:2509.17099, 2025. 

    5.) D. Blanco. Proving periodic solutions and branches in the 2D Swift Hohenberg PDE with hexagonal and triangular symmetry. arXiv:2602.12491, 2026. 

    6.) D. Blanco and J.P. Lessard. Rigorous Validation of Cusp Bifurcations of Stationary Periodic Solutions in Partial Differential Equations. arxiv:2608.15613, 2026.

    Undergraduate/Masters Thesis:

    D. Blanco (Advised by J. Mireles-James, Y. Fily, and K. Nur-tegin). The Sitnikov Problem, Low Energy Transfers, and the Economic Feasibility of Asteroid Mining. Honors Student Theses. Florida Atlantic University. 2022.

    Ph.D. Thesis:

    D. Blanco (Advised by J.P. Lessard).  Extensions in Computer-Assisted Analysis for Partial Differential Equations Posed on Unbounded Domains. Department of Mathematics and Statistics. McGill University. (To appear in 2026).