Photo cred to Cynthia Guo

Max Hopkins

La Jolla, CA, 92092
Office 4232

nmhopkin @ eng dot ucsd dot edu


I am a third-year PhD student in the theory group at UCSD, where I am advised by Daniel Kane and Shachar Lovett and supported by NSF and Jacobs Fellowships. 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.

I co-host the weekly UCSD Theory Lunch on Thursday's with Sam Mcguire. Past and upcoming talks can be found here.

My work mostly focuses on the intersection of learning theory and computational geometry, and especially on how and when asking better questions empowers us to learn more efficiently. If you're interested and/or new to this area, check out this recent blog post for a basic primer, which covers how the ability to compare data can drastically speed up and robustify learning! More recently, I have also been working on higher-order random walks on high dimensional expanders, and am especially interested in their connections to CSP-approximation and Unique Games.

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


Conference Papers

  1. The Power of Comparisons for Actively Learning Linear Separators
    Max Hopkins, Daniel Kane, Shachar Lovett
    NeurIPS 2020

  2. Point Location and Active Learning: Learning Halfspaces Almost Optimally
    Max Hopkins, Daniel Kane, Shachar Lovett, Gaurav Mahajan
    FOCS 2020

  3. Noise Tolerant, Reliable Active Classification with Comparison Queries
    Max Hopkins, Daniel Kane, Shachar Lovett, Gaurav Mahajan
    COLT 2020

  4. Doppelgangers: the Ur-Operation and Posets of Bounded Height
    Thomas Browning, Max Hopkins, Zander Kelley
    Extended Abstract appeared in Proceedings of FPSAC 2018

  5. Simulated Annealing for JPEG Quantization
    Max Hopkins, Michael Mitzenmacher, Sebastian Wagner-Carena
    DCC 2018 (poster)

Journal Papers

  1. A Novel CMB Component Separation Method: Hierarchical Generalized Morphological Component Analysis
    Sebastian Wagner-Carena, Max Hopkins, Ana Rivero, Cora Dvorkin
    MNRAS, May 2020



  1. Beyond the Spectral Gap: Pseudorandomness and High Dimensional Expansion
    Max Hopkins, Tali Kaufman, Shachar Lovett
    In Preparation

Miscellaneous Writing


  • UCSD Theory Seminar or Lunch

    • Small Set Expansion in the Johnson Graph through High Dimensional Expansion (Fall '19)

    • High Dimensional Expanders: The Basics (Summer '19)

    • Reasoning in the Presence of Noise (Spring '19)

    • The Power of Comparisons for Active Learning (Winter '18)

  • Undergraduate Talks

    • On the Cohomology of Dihedral Groups (Spring '17)

    • Understanding Doppelgangers and the Ur-Operation (Summer '16)


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

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