I am a third year PhD student at Duke University. My advisor is Alexander Dunlap. I completed my undergraduate degree at the University of Arizona and Mesa Community College.
I am broadly interested in connections between PDE and Probability. Some particular interests are:
Critical (S)PDE
Reaction Diffusion Equations
Fluid Dynamics
Statistical Mechanics
Email: Bryan.Castillo@duke.edu
McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data. Bryan Castillo and Alexander Dunlap, arXiv preprint: arXiv:2509.06260
Undergraduate:
Comparing embedded graphs using average branching distance. Levent Batakci, Abigail Branson, Bryan Castillo, Candace Todd, Erin Wolf Chambers, Elizabeth Munch, Involve Journal of Mathematics (2023)
Brutus read it so I don't have to
Winter 2025-2026 SPDE reading group (co-organizer)
Presentations:
Energy solutions of singular SPDEs (Gräfner, Perkowski)
Fall 2025, fluids reading group (co-organizer)
Presentations:
Global well-posedness for the critical 2D dissipative quasi-geostrophic equation (Kiselev,Nazarov,Volberg)
Anomalous dissapation via spontaneous stochasticity with a two-dimensional velocity field (Johansson, Sorella)
Summer 2025, statistical mechanics reading group (co-organizer)
Presentations:
Statistical hydrodynamics (Onsager)
Spring 2025, fluids reading group
Presentations:
Long-time confinement near special vortex crystals (Donati)
Fall 2024, High-dimensional probability reading group
Presentations:
Curvature-dimension conditions for Poincaré inequalities (based on Analysis and geometry of Markov diffusion operators by Bakry, Gentile, Ledoux)
Fall 2024, Fluids reading group
Presentations:
Minimal cones and the Bernstein problem (Bombieri, De Giorgi, Giusti) - An amazing paper!
Summer 2024, Log-sobolev inequality reading group (co-organizer)
Presentations:
Topics from analysis and geometry of Markov diffusion operators (Bakry, Gentile, Ledoux)
Spring 2024, Fluids reading group
Presentations:
The twisting tennis racket (Ashbaugh, Chicone, Cushman)
I co-organize a running and lifting club at Duke. Here are some of my current personal records:
Squat: 425 lb
Bench Press: 265 lb
C&j (Olympic lift): 135 kg
Snatch (Olympic lift): 101 kg
5k time: 31m 40s
Climbing gym difficulty: V1+
Here is a photo from our first 5k race together. From left to right: Me, Joel Greenfield (the winner!), Zach Turner, Naji Sarsam, David Koralov
Spring 2026: Discussion leader - Math 202 Multivariable Calculus for Economics