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

I’m advised by Boris Hanin and work closely with Gautam Reddy. I’m grateful to be supported by the Department of Energy Computational Science Graduate Fellowship (DOE CSGF).

You can find my C.V. here 📄.

## I think about the mathematics of high-dimensional nonlinear systems that organize, compute, and learn.

Somehow, I don’t care whether these systems are neuronal, algorithmic, made of particles, or something else entirely — I’m interested in the universal mathematical and statistical structures underlying their function.

I like to frame these ideas in light of an ambient question:

What mathematical structure distinguishes “life” and “mind” from the matter (and energy) that composes them?

Some topics occupying me lately:

- mathematical deep learning theory and statistical learning theory
- statistical mechanics of complex biological systems
- theoretical neuroscience

I’m also generally excited by mathematics that live in the convex hull formed by the following areas:

- high-dimensional phenomena in probability and statistics
- interacting particle systems
- random matrix theory

### Contact

- email: an4386[at]princeton[dot]edu
- twitter: @algomage

## Previous adventures

- [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.

My name:

- IPA pronunciation: ˈælɪks neˈgroʊn
- Lately I’m noticing a high concentration of Alex’s in the fields in which I participate. To disambiguate, if I run into several Alex’s at a conference, I might switch to Alejandro. To be precise, let us agree my first name is actually

🚧 🚧 🚧

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