Lucas Chen
Lucas Chen
email: lucasch | at | uchicago | dot | edu. CV
email: lucasch | at | uchicago | dot | edu. CV
I am a third-year math major at the University of Chicago. I'm excited about studying geometry (in many forms). I am concerned about AI safety and think often about the theory of interpretability and AI policy.
Some other interests of mine include anthropology and robotics. I'm hoping to improve my expository and opinion writing!
Currently:
(Very slowly) trying to read Peter May's books/notes on algebraic topology, and Galois Groups and Fundamental Groups by Tamás Szamuely.
My math interests run a wide range, but I like anything I can visually picture dynamically and in detail. Recently this has meant a lot of interest in incidence geometry and monodromy representations.
Some recs:
Algebraic geometry:
I enjoyed Mumford's red book a lot. For the undergrad AG elective I took Spring 2026, we also had Görtz-Wedhorn's two volumes as references, which were comprehensive but better exposition than Stacks and had nicer exercises.
Analysis:
I think Pugh's Real Mathematical Analysis is pretty good and is exciting because the exercises do a great job of convincing you analysis is batshit insane.
Differential geometry:
An opinion I've heard a few times is that differential geometry is a terrible subject to learn from a comprehensive textbook, and having tried to with about three separate pronounced efforts I kind of agree.
Nonetheless I think everyone should know differential topology, so I basically have to recommend anything by Milnor or Chern.
Preprints:
Completed at SMALL REU:
The Bias Conjecture for One-Parameter, Non-Isotrivial Elliptic Curve Families, joint with Joshua Im, Steven J. Miller, Devayani Pradhan. arxiv
Bounding The Number of Zeros Near the Central Point in Families of Cuspidal Newforms, joint with Christopher Housholder, Joshua Khan, Steven J. Miller, Devayani Pradhan. arxiv
On the Existence of Hyperelliptic Curves over $\mathbb Q(T)$ with Certain Jacobian Ranks, joint with Joshua Im, Steven J. Miller, Devayani Pradhan. arxiv
AI safety: I believe controlled, interpretable AI is currently an urgent concern which benefits from technical, policy, and theoretical expertise. Some helpful starting points I'd vouch for:
I also feel that academics should more than ever now be called on to make their voices heard politically.
Some research/academic resources:
Vakil's three things for getting value out of math talks (lol)
Growing up in New York I gained a lot from a few amazing math programs and organizations:
My favorite literary works as of right now are Hurricane Season by Fernanda Melchor, Speaker for the Dead by Orson Scott Card*, and Hippolytus by Euripides.
I love a lot of kinds of music and am currently listening to a lot of yeule.
Some movies I love are Blade Runner, If I Had Legs I'd Kick You, Heathers, and My Left Eye Sees Ghosts.
*note: I can't recommend anyone pay money for Card's books while he continues to consistently punch down from his platform. however, I do feel that trying to reconcile the author to his own book remains somewhat fascinating.