Mathematical Physicist (PhD)

Role Overview

Contribute to CritPt, a public benchmark of research-level physics challenges designed to evaluate whether frontier AI models can perform genuine physics research reasoning. Review the benchmark paper, arXiv:2509.26574, before applying to understand the nature of the work.

This is research-grade work in which each submission must provide complete written reasoning that another specialist can independently follow and verify. The expected standard of proof is closer to mathematics than typical physics work.

Key Responsibilities

• Undertake assignments in your published area of specialization, including creating research problems, solving problems, reviewing completed work, or auditing work.
• Develop rigorous, independently verifiable written arguments for research-level physics challenges.
• Work on an assignment agreed after matching your publication record to a specific research area.

Research Areas

• Special functions, including hypergeometric identities and analytic continuation, Gaussian hypergeometric functions, parameter differentiation, quadratic transformations, series-index continuation, digamma-function series, and asymptotic or series expansions.
• Integrable systems, including half-wave maps, Lax pairs, isospectral flows, Haldane-Shastry and Calogero-Moser systems, Hilbert transforms, singular integral operators, conserved-charge hierarchies, solitons, and numerical quadrature of singular integrals.
• Permutation combinatorics for random tensor network entanglement, including Cayley distance, symmetric-group geodesics, minimal permutation factorizations, non-crossing partitions, replica permutation spin models, Weingarten calculus, multipartite entanglement measures, and combinatorial enumeration.
• Conformal geometry, including Fefferman-Graham ambient metrics, Weyl covariance, obstruction tensors, Schouten and Weyl curvature tensors, Ricci-flatness solutions, dimensional-continuation poles and residues, and Poincare-Einstein asymptotic expansions.

Qualifications

• PhD in mathematical physics, theoretical physics, or mathematics. Postdoctoral researchers, research scientists, and junior faculty are especially well suited; senior PhD students with a strong first-author record may apply.
• Published research on at least one listed phenomenon itself, not merely an adjacent topic or related method.
• A verifiable record of three to five representative papers, preferably from the last five years, with arXiv IDs or DOIs. First-author publications are strongly preferred.
• Publications demonstrating at least one relevant method family: special-function analysis, integrability, combinatorial methods, or geometric methods described above.
• Working proficiency with LaTeX, Python, SymPy, and Jupyter. Familiarity with an agentic coding extension in VS Code is useful; candidly disclosed gaps are acceptable.
• English proficiency at B2 level or above, including clear written technical reasoning.

Work Terms

• Remote, asynchronous hourly engagement with no fixed working hours.
• Commit approximately 10 hours per week for an 8 to 10 week period, beginning immediately.

Compensation

$80 to $110 per hour, based on the depth of your match to the relevant subdomain.

Application Process

• Complete the application form with your education, research experience, method self-assessment, and up to five areas that best match your expertise.
• For every selected area, provide an arXiv ID or DOI for your own publication, your author position, and the methods demonstrated. Selections without supporting evidence are not scored.
• Your publications and authorship will be verified against public records.
• Qualified applicants may proceed directly to assignment matching or be invited to a short live alignment call to agree the research area and assignment.
• A 30 to 45 minute assessment may be requested when needed, though most applicants will not complete one.