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:
(S)PDE in critical dimension
Reaction Diffusion Equations
Fluid Dynamics
Statistical Mechanics
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)
Reading groups and activities
Reading groups and activities
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
5k time: 31m 40s
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
Conference and seminar talks
Conference and seminar talks
November 2025
Triangle computational and applied mathematics symposium, NC State University, Raleigh, North Carolina
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