Dr. Viator hails from southern Louisiana, where he spent most of his childhood and young adult life. After finishing his PhD in Mathematics at Louisiana State University in 2016, he spent time as a postdoctoral researcher at the Institute for Mathematics and its Applications (Minneapolis, MN), as well as a visiting professor at Southern Methodist University (Dallas, TX) and Swarthmore College (Swarthmore, PA), where he discovered a deep love for liberal arts education. It was that love for student engagement and undergraduate learning that led him to Denison.
Dr. Viator spends his afternoons and weekends expanding his culinary repertoire, reading fantasy/sci-fi novels, and playing board and video games with friends locally and across the country.
Learning & Teaching
- Math 135 - Single Variable Calculus
- Postdoctoral Researcher - Institute for Math and its Applications (2016-2017)
- Visiting Assistant Professor - Southern Methodist University (2017-2020)
- Visiting Assistant Professor - Swarthmore College (2020-2023)
- Assistant Professor - Denison University (2023-)
Research
My research specifically focuses on the application of spectral theory and perturbation theory to problems in applied partial differential equations which model wave propagation (e.g. acoustic, electromagnetic) through various composite material designs. My dissertation established a rigorous, explicit lower bound on the size of band-gaps in the frequency spectrum of 2-dimensional high-contrast photonic crystals, given explicitly in terms of the crystal geometry (and corresponding eigenvalue problems) and a finite contrast ratio. Recent further developments have included an partial extension of this work to 3-dimensional photonic crystals; there, Maxwell's equations do not simplify into a divergence-form scalar equation, and more sophisticated analysis is necessary to describe the frequency spectrum of the crystal.
More recently, I have also been interested in geometric spectral optimization problems. Specifically, I have published results on the Steklov eigenvalue problem (used to describe fluid sloshing, energy dissipation in conductive composites, and more) for nearly-spherical spherical domains, which conclude with a local optimization result for an infinite list of higher Steklov eigenvalues.