Hello

I am currently a postdoctoral researcher in the Department of Mathematics and Statistics at the University of Western Australia.

My research interests are in nonlinear and/or nonlocal partial differential equations arising from phase transitions and shape optimisation. In particular, I am interested in free boundary problems, nonlocal minimal surfaces, and overdetermined problems.

In July 2025, I was awarded my PhD from the University of Western Australia under the supervision of Enrico Valdinoci (principal supervisor), Serena Dipierro, and Giorgio Poggesi.

Contact details

Email: jack.thompson@uwa.edu.au
Address: Department of Mathematics and Statistics. 35 Stirling Highway, Perth, WA 6009, Australia
Office: G1.11, Mathematics building.

Links

UWA website
CV
ArXiv
ORCID
Google Scholar

Publications and preprints

Preprints

  1. Volumetric density estimates for nonlocal minimal surfaces, pdf
    Mateusz Kwaśnicki, Jack Thompson
    Submitted, available on arXiv (2026)
  2. A half-space theorem for nonlocal minimal surfaces, pdf
    Matteo Cozzi, Jack Thompson
    Submitted, available on arXiv (2026)
  3. Quantitative stability for the nonlocal overdetermined Serrin problem, pdf
    Serena Dipierro, Giorgio Poggesi, Jack Thompson, Enrico Valdinoci
    Submitted, available on arXiv (2023)

Publications

  1. Density estimates and the fractional Sobolev inequality for sets of zero s-mean curvature, pdf
    Jack Thompson
    Calc. Var. 65, 2 (2026).
  2. The nonlocal Harnack inequality for antisymmetric functions: an approach via Bochner's relation and harmonic analysis, pdf
    Serena Dipierro, Mateusz Kwaśnicki, Jack Thompson, Enrico Valdinoci
    Comm. Partial Differential Equations 50.8 (2025), pp. 1074–1098
  3. Some nonlocal formulas inspired by an identity of James Simon, pdf
    Serena Dipierro, Jack Thompson, Enrico Valdinoci
    Münster J. Math. 18 (2025), p.201-226.
  4. Quantitative stability for overdetermined nonlocal problems with parallel surfaces and investigation of the stability exponents, pdf
    Serena Dipierro, Giorgio Poggesi Jack Thompson, Enrico Valdinoci
    J. Math Pures Appl. (9) 188 (2024), p.273-319
  5. On the Harnack inequality for antisymmetric s-harmonic functions, pdf
    Serena Dipierro, Jack Thompson, Enrico Valdinoci
    J. Funct. Anal. 285 (2023), Paper No. 109917, p.49
  6. The role of antisymmetric functions in nonlocal equations, pdf
    Serena Dipierro, Giorgio Poggesi, Jack Thompson, Enrico Valdinoci
    Trans. Amer. Math. Soc. 377 (2024), p.1671-1692

PhD Thesis

  1. Stability results for nonlocal Serrin-type problems, antisymmetric Harnack inequalities, and geometric estimates, pdf
    Supervisors: Enrico Valdinoci (principal supervisor), Serena Dipierro, Giorgio Poggesi
    Available on arXiv. Awarded July 2025.

Teaching

Here is a complete list of my current and previous teaching:

Course coordinator at the University of Western Australia

  • Semester 2, 2025: MATH1720 Mathematics Fundamentals
  • Semester 2, 2024: MATH1720 Mathematics Fundamentals

Assistant to course coordinator at the University of Western Australia

  • Semester 2, 2022: MATH1012 Mathematical Theory and Methods
  • Semester 1, 2022: MATH1012 Mathematical Theory and Methods

Teaching assistant at the University of Western Australia

  • 2024 Semester 1: MATH1012 Mathematical Theory and Methods (two classes)
  • 2023 Semester 2: MATH1012 Mathematical Theory and Methods
  • 2023 Semester 1: MATH1011 Multivariable Calculus, MATH1013 Mathematical Analysis, MATH1700 Forensic Mathematics
  • 2022 Semester 1: MATH1012 Mathematical Theory and Methods
  • 2021 Semester 2: MATH3032 Topology and Analysis, MATH1012 Mathematical Theory and Methods (two classes)
  • 2021 Semester 1: MATH1011 Multivariable Calculus, MATH1721 Mathematics Foundations: Methods

Teaching assistant at the University of Queensland

  • 2021 Semester 1: MATH2001 Calculus & Linear Algebra II (two online classes)
  • 2020 Semester 2: MATH3405 Differential Geometry, MATH1061 Discrete Mathematics
  • 2020 Semester 1: STAT3004 Probability Models & Stochastic Processes (two classes), STAT2003 Mathemtical Probability, MATH2000 Linear Algebra II
  • 2019 Semester 2: MATH1061 Discrete Mathematics
  • 2019 Semester 1: MATH1071 Advanced Calculus & Linear Algebra