Judson Kuhrman

Department of Mathematics · Stanford University

Office 380-380M · kuhrman@stanford.edu

Research Interests: Geometric Topology; 4-manifolds and Knotted Surfaces; Seiberg–Witten Invariants.

Education

PhD, Mathematics

Stanford University

Advisor: Ciprian Manolescu

2022 – present

BA, Mathematics

University of Chicago

2018 – 2022

Papers & Preprints

  1. Miyazawa's Invariant, Lefschetz Numbers, and Seifert Solids. preprint, 2026.[arXiv:2605.14996]
  2. More Exotic $\mathbb{RP}^2$-knots and Homotopy Spheres. preprint; under review at MRL, 2025.[arXiv:2507.03798]

Talks & Presentations

  • Miyazawa's Invariant and Seifert Solids (10-min. talk). New Structures in Low-Dimensional Topology Workshop 2026—AIM.
    June 2026
  • Knotted Surfaces and Real Seiberg–Witten Theory. Stanford Topology Seminar.
    March 2026
  • Knotted Surfaces and Real Seiberg–Witten Theory. Gauge Theory Virtual Seminar.
    January 2026
  • Spinning Constructions and Exotic $\mathbb{RP}^2$-knots. UC Berkeley Topology Seminar.
    December 2025
  • Spinning Constructions and Exotic $\mathbb{RP}^2$-knots. UT Austin Topology Seminar.
    October 2025
  • (Lightning Talk). Trisectors Workshop 2025.
    July 2025

Teaching

  • CA: MATH 149: Topology, Computation, and Data, Stanford
    Winter 2026
  • TA: MATH 51: Linear Algebra, Multivariable Calculus, and Modern Applications, Stanford
    Fall 2025
  • TA: MATH 63CM: Modern Mathematics: Continuous Methods, Stanford
    Spring 2025
  • CA: MATH 116: Complex Analysis, Stanford
    Fall 2024
  • TA: MATH 53: Differential Equations with Linear Algebra, Fourier Methods, and Modern Applications, Stanford
    Spring 2024
  • CA: MATH 144: Introduction to Topology and Geometry, Stanford
    Winter 2024
  • CA: MATH 147: Differential Topology, Stanford
    Spring 2023
  • CA: MATH 106: Functions of a Complex Variable, Stanford
    Fall 2022
  • Junior Tutor: MATH 13000 Sequence, UChicago
    2021-22
  • Junior Tutor: MATH 16000 IBL Sequence, UChicago
    2020-21
  • VCA: MATH 15000 Sequence, UChicago
    2019-20

Awards & Honors

  • Paul R. Cohen Prize, University of Chicago Department of Mathematics
    2022

Service & Outreach

  • Stanford Graduate Workers Union: currently elected as Steward and Trustee; formerly served as Sciences Area Chief Steward from Spring 2025 to Spring 2026
  • Stanford Student Topology Seminar: Co-organized 2024–25; joint with Qianhe Qin
  • Stanford Math DRP: Mentored several undergraduate students since 2023
  • Beers (now officially known as Stanford Math Grad Social): Co-organized department happy hours 2023–24; joint with Hamish Blair, Alex Lopez, and Andy Yin