@ Culver City, 2026
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I am a fourth year PhD student at the UC Berkeley Math department, where I am advised by Professor Sunčica Čanić. My research interests lie in deterministic and stochastic nonlinear PDEs arising in fluid dynamics and collective behavior, with a primary focus on well-posedness theory. I completed my B.A. in Mathematics with a minor in Computer Science at New York University in 2022.
Contact: amy_dai@berkeley.edu
Office: Evans 1006
A remark on my name: I go by "Amy" in an English speaking environment, but I publish under "Rongyi Dai", which is the pinyin spelling of my name "戴蓉仪"， pronounced as "DAI-Ron-Yee".
Research
Research
Stochastic Compressible Euler Equations with Frictional Damping: Existence of L^\infty Martingale Solutions and Asymptotic Porous Medium-Like Behavior, joint with J. Kuan, K. Tawri, S. Čanić, K. Trivisa (2026). submitted. [arxiv]
Activities
Activities
Conferences and Workshops
Conferences and Workshops
ICERM Workshop: PDEs for Many Particle System, ICERM, Providence, USA, Aug 2026:
Poster given: "Existence and long time behavior of solutions to stochastic isentropic Euler equation with frictional damping in 1D" [Poster]
RTG Summer School: Interface of Probability and PDE, CMU, Pittsburg, USA, June 2026:
Poster given: "Existence and long time behavior of solutions to stochastic isentropic Euler equation with frictional damping in 1D"
International Conference on Hyperbolic Problems, Stuttgart, Germany, May 2026
Talk given: "Existence and long time behavior of solutions to stochastic isentropic Euler equation with frictional damping in 1D"
Southern California Applied Mathematics Symposium, Los Angeles, USA, April 2026
Talk given: "Existence and long time behavior of solutions to stochastic isentropic Euler equation with frictional damping in 1D"
Seminar Talks
Seminar Talks
"Existence and long time behavior of solutions to stochastic isentropic Euler equation with frictional damping in 1D", Applied PDE Seminar, UC Berkeley, November 2025.
Expository Talk: "Loss of regularity for the continuity equation with non-Lipschitz fields", Fluid Dynamics Learning Seminar, UC Berkeley, December 2025. [Notes]
Expository Talk: "BV solutions to system of hyperbolic conservation laws in one dimension", Nonlinear PDE Learning Seminar, UC Berkeley, Mar 2024. [Notes]
Expository Talk: "Introduction to hyperbolic conservation laws", Applied PDE Seminar, UC Berkeley, Jan 2023. [Slides]
Organization and Mentorship
Organization and Mentorship
I organize the Applied PDE Seminar in Fall 2025 and Spring 2026.
I mentored undergraduate math students on independent reading projects through the Directed Reading Program in Fall 2024, Spring 2025, and Spring 2026.
Teaching
Teaching
Spring 2026: I am on Department Spring Fellowship this semester.
Fall 2025: GSI for Math 55: Discrete Mathematics.
Spring 2025: Head GSI for Math 16A: Analytic Geometry and Calculus.
Fall 2024: GSI for Math 32: Precalculus.
Spring 2024: Head GSI for Math 1B: Calculus II .
Fall 2023: Head GSI for Math 1A: Calculus I .
Spring 2023: GSI for Math 1B: Calculus II .
Fall 2022: GSI for Math 1A: Calculus I .
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