I’m a mathematical scientist doing my PhD in the Program in Applied and Computational Mathematics (PACM) at Princeton University.
My advisor is Boris Hanin and my work is supported by the Department of Energy Computational Science Graduate Fellowship (DOE CSGF). I feel incredibly lucky, and I’m grateful for the mentorship and freedom my advisor, program, and fellowship afford me.
Contact
- email: an4386[at]princeton[dot]edu
- twitter: @negronax
- C.V. 📄
I study high-dimensional, nonlinear systems that organize, learn, and compute. I draw from ideas seeded in probability theory, mathematical physics, and partial differential equations to understand how collective behavior emerges from many interacting components.
Recently, my passion is for mathematical phenomena that percolate up from a range of scientific and engineering applications. Current examples in my work include deep learning, disordered dynamics in high dimension, biological neural computation, and unconventional/analog computing.
Active (~Fall ‘26) research topics
- mathematical foundations of deep learning, especially scaling limits and the dynamics of deep neural networks in feature-learning regime;
- mathematical principles underlying hyperparameter transfer;
- the theory and practice of thermodynamic computing;
- nonlinear PDE models of computation in biological neural systems.
Subjects I find particularly beautiful and fun to learn about:
- random matrix theory
- spin glasses and disordered systems
- interacting particle systems and kinetic equations (especially emerging tools for non-exchangeable particle systems)
- stochastic PDEs in mathematical physics
- developmental biology and morphogenesis
- theoretical and computational neuroscience
Other random things I like:
- formalization in Lean
- energy-based algorithms and probabilistic hardware
- hockey and American football (go Bills)
- techno and house music 🎚️
Previous chapters
- [2022 - 2024] K. Lisa Yang Post-baccalaureate Research Scholar at MIT in the Brain and Cognitive Sciences department, advised by Ila Fiete
- [2021 - 2022] Simons Foundation Shenoy Undergraduate Research Fellow at the University of Chicago, advised by Brent Doiron
- I earned a B.S. in Applied Mathematics, B.S. in Statistics from the Illinois Institute of Technology, advised by Sergey Nadtochiy
- In a previous life, I wrote poetry and fiction at Northwestern University and studied Classics.
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This site hosts my academic work, but I intend to write about other things too.