Bryan Castillo
Bryan Castillo
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About Me
About Me
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
Fluid Dynamics
Statistical Mechanics
Reaction Diffusion Equations
Grönwall inequalities
Email: Bryan.Castillo@duke.edu
Research
Research
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
Invited talks and reading group presentations
Invited talks and reading group presentations
Reaction diffusion equations with random initial data. Spring 2026 BIRS workshop on Localization, Delocalization, and Diffusion in Disordered Systems
Introduction to PDEs and Waves for the Atmosphere and Ocean (Majda). Spring 2026 Fluids reading group (on geophysical flows)
The Poincaré–Bendixson theorem and some applications to fluids. Spring 2026 Topological fluid dynamics reading group.
Energy solutions of singular SPDEs (Gräfner, Perkowski). Winter 2025-2026 SPDE reading group (co-organizer)
Global well-posedness for the critical 2D dissipative quasi-geostrophic equation (Kiselev,Nazarov,Volberg). Fall 2025, fluids reading group (co-organizer)
Anomalous dissapation via spontaneous stochasticity with a two-dimensional velocity field (Johansson, Sorella). Fall 2025, fluids reading group (co-organizer)
Statistical hydrodynamics (Onsager). Summer 2025, statistical mechanics reading group (co-organizer)
Long-time confinement near special vortex crystals (Donati). Spring 2025, fluids reading group
Curvature-dimension conditions for Poincaré inequalities (based on Analysis and geometry of Markov diffusion operators by Bakry, Gentile, Ledoux). Fall 2024, High-dimensional probability reading group
Minimal cones and the Bernstein problem (Bombieri, De Giorgi, Giusti) - An amazing paper! Fall 2024, Fluids reading group
Topics from analysis and geometry of Markov diffusion operators (Bakry, Gentile, Ledoux). Summer 2024, Log-sobolev inequality reading group (co-organizer)
The twisting tennis racket (Ashbaugh, Chicone, Cushman). Spring 2024, Fluids reading group
Miscellany
Miscellany
Days without McDonalds: 12
Green Tea counter (since 4/19/2026): 19
Current personal records:
Squat: 425 lb
Bench Press: 265 lb
Deadlift: 435 lb
C&j (Olympic lift): 135 kg
Snatch (Olympic lift): 101 kg
5k time: 31m 40s
Climbing gym difficulty: V1+
League of Legends rank: Master tier (low lp) (support main)
preliminary exams passed : 1/1
Some achievements of my students (in weightlifting):
Naji Sarsam: 215 lb squat (almost 2x b.w.)
David Koralov: 225 lb bench press
Zach Turner: 135 lb bench press
Winner of the first Duke running/weightlifting club 5k: Joel Greenfield
Teaching
Teaching
Fall 2024: Lab TA - Math 111 Calculus 1
Spring 2026: Discussion leader - Math 202 Multivariable Calculus for Economics
Acknowledgements
Acknowledgements
None of my achievements would have been possible without the guidence and support of my friends and mentors. Here are a few of the friendly people who helped shape my mathematical career:
Adam Avilez (Mesa community college)
Christopher Henderson (University of Maryland)
Alexander Dunlap (Duke university)
Tarek Elgindi (Duke university)
Jonathan Mattingly (Duke university)
Brutus (the cat)
Naji Sarsam (Duke University)
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