Photo cred to Cynthia Guo

Max Hopkins

Princeton-IAS
mh4067 @ princeton dot edu

About

Hi! I'm a postdoctoral associate of the Princeton theory group ('24-'25) and CSDM at the Institute for Advanced Study ('25-'27). Prior to this I was fortunate to recieve my PhD under Daniel Kane and Shachar Lovett at UCSD, a year of which I was equally fortunate to spend at the Weizmann Institute with Irit Dinur, and as a Research Fellow at the Simons Institute for the Theory of Computation (Summer '23). Even prior to this, I received a BA in mathematics at Harvard University, where I was lucky to work under Michael Mitzenmacher and Madhu Sudan. My research has been generously supported by NSF GRFP, ARCS, and JSOE fellowships.

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

Interests

I am broadly interested in areas such as computational complexity, algorithms, boolean function analysis, statistical and computational learning theory, algorithmic stability, and computational geometry. Currently, I mostly think about:

  1. High Dimensional Expanders in Computation
  2. High Dimensional Expansion (HDX) is an emerging area in computer science and mathematics with a wide range of applications across complexity, approximate sampling, (quantum) error correction, and more. I study analysis of boolean functions and random walks on HDX, especially in the context of error correction and computational complexity. If you are here looking for introductory material on HDX, see:


  3. Learning Theory
  4. I study a broad set of topics within learning including algorithmic stability (e.g. notions like replicability and differential privacy), learning with non-traditional query data (e.g. with comparison data), active learning, and learning beyond traditional uniform convergence guarantees. I am most interested in understanding how such notions relate to underlying combinatorial and geometric structure of data.

Service

Papers

Author order is alphabetical (unless otherwise stated)

Preprints

  • From Generative to Episodic: Sample-Efficient Replicable RL
    Max Hopkins, Sihan Liu, Christopher Ye, Yuichi Yoshida
    Coming soon!

Publications

Blog Posts

Miscellaneous Writing

Talks

Upcoming Talks
  • STOC HDX Workshop: June 23

Invited Talks
  • The Geometry of Stable Mean Estimation (MIT Combinatorics Seminar)

  • Chernoff Bounds on HDX and their Applications (UW Theory Seminar, Cornell Junior Theorists Day, Princeton Theory Lunch, JHU Theory Seminar, IAS CSDM Seminar, ICTS HDX & Codes, CanaDAM)

  • Explicit SoS Lower Bounds from High Dimensional Expanders (Simons Institute, UCSD Theory Seminar, UToronto Theory Seminar, CMU HDX Reading Group, IAS CSDM Seminar)

  • Boolean Analysis on HDX (Simons Institute Bootcamp Tutorial)

  • 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, Weizmann Guest Lecture, Ben-Gurion Theory Seminar)

  • Realizable Learning is All You Need (COLT '22, UWaterloo Student Seminar, GaTech Student Seminar, Harvard Student Seminar, Stanford Theory Lunch, Weizmann Theory Lunch, TTIC/Northwestern Junior Theorists Workshop)

  • High Dimensional Expanders and Unique Games (SODA '22, UW Theory 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)

  • The Power of Comparisons for Active Learning (UCSD Theory Seminar)

UCSD Theory Lunch
  • Chernoff Bounds on HDX

  • Explicit SoS Lower bounds from HDX

  • 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

Undergraduate Talks
  • On the Cohomology of Dihedral Groups

  • Understanding Doppelgangers and the Ur-Operation

Teaching

At UCSD
  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.