Photo cred to Cynthia Guo

Max Hopkins

La Jolla, CA, 92092
Office 4232

nmhopkin @ eng dot ucsd dot edu


I am a PhD student in the theory group at UCSD where I am thankful to be advised by Daniel Kane and Shachar Lovett. I did my undergraduate BA in Mathematics at Harvard University with a minor in Computer Science. In my time there, I was lucky enough to work under Michael Mitzenmacher and Madhu Sudan. My research is generously supported by NSF GRFP, ARCS, and JSOE fellowships.

I am currently a visiting student at the Weizmann Institute (Ziskind 205).

If you are looking for UCSD Theory Lunch, it has been passed to the next generation.

I like singing, boardgames, squash, and sushi (in no particular order).


I am broadly interested in areas such as learning theory, computational geometry, combinatorics, approximation algorithms, and hardness of approximation. Currently, I mostly think about:

  1. High Dimensional Expanders
  2. High Dimensional Expansion (HDX) is an emerging area with applications across topics such as sampling, error correction, approximation algorithms, and more. I study analysis of boolean functions and random walks on HDX, especially in the context of hardness of approximation. In Spring 2021, Shachar Lovett and I co-taught an introductory course on expanders and HDX. Detailed course notes can be found here, and corresponding lectures here.

  3. Learning beyond Uniform Convergence
  4. Many classical results in learning theory rely on the idea of uniform convergence, that empirical risk should converge to true risk across all hypotheses simultaneously. Unfortunately, this paradigm fails in more practical settings beyond basic worst-case analysis. I am interested in studying learnability in more realistic settings like learning with arbitrary distributional assumptions where these traditional techniques fail.

  5. Active Learning through Enriched Queries
  6. When does adaptivity help us learn? In standard models, it is well known that adaptivity often provides no asymptotic benefit. I study how asking better questions allows us to build adaptive algorithms that drastically speed up learning. If you're interested in this area, check out this blog post for a basic primer.


(Author order is alphabetical)


Conference Papers

Journal Papers

Blog Posts

Miscellaneous Writing


Upcoming Talks
Invited Talks
  • On High Dimensional Expanders and Hardness of Approximation (IISC Bangalore)

  • Hypercontractivity on High Dimensional Expanders (STOC '22, TTIC, UMich Theory Seminar, MIT A&C Seminar)

  • Realizable Learning is All You Need (COLT '22, UWaterloo, GaTech Student Seminars, Stanford Theory Lunch)

  • High Dimensional Expanders and Unique Games (SODA '22, UW Seminar, SoS+TCS Seminar, Cornell Theory Tea, Chicago/TTIC (Reading Group))

  • Active Learning in Bounded Memory (COLT '21)

  • Point Location and Active Learning (FOCS '20, Harvard CMSA)

  • Noise Tolerant Active Learning with Comparisons (COLT '20)

UCSD Theory Seminar/Lunch
  • On the Equivalence of Realizable and Agnostic Learning

  • Active Learning with Bounded Memory

  • Point Location and Active Learning

  • An Open Problem in Noisy Sorting

  • Small Set Expansion in the Johnson Graph through High Dimensional Expansion

  • High Dimensional Expanders: The Basics

  • Reasoning in the Presence of Noise

  • The Power of Comparisons for Active Learning

Undergraduate Talks
  • On the Cohomology of Dihedral Groups

  • Understanding Doppelgangers and the Ur-Operation


  1. Co-taught CSE 291, Expander graphs and high-dimensional expanders, Spring 2021.

  2. TA for CSE 200, Computability and Complexity, Winter 2020.

At Harvard
  1. TA for APMTH 106, Applied Algebra, Fall 2017.