Alex Negrón

I am a mathematical scientist doing my PhD in the Program in Applied and Computational Mathematics (PACM) at Princeton University.

I’m advised by 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 think about the mathematics of high-dimensional, non-linear systems that organize, learn, and compute.

I study these systems with ideas seeded along the interface of probability theory and partial differential equations. I get excited when I see the same mathematical structures percolating up from diverse scientific and engineering applications, like deep learning, high-dimensional statistics, biological neural computation, disordered systems, and developmental biology.

Active (~April ‘26) research topics

  • mathematical foundations of deep/machine learning
  • nonlinear PDEs in models of biological neural computation

Subjects I find particularly beautiful and fun to learn about:

  • random matrix theory
  • spin glasses and disordered systems
  • interacting particle systems and kinetic equations
  • 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




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This site hosts my academic work, but I intend to write about other things too.