Mathematical Physicist (PhD)

Role Overview

Contribute to a public benchmark of research-level physics challenges designed to evaluate frontier AI reasoning beyond textbook problem solving. Review the CritPt benchmark paper, arXiv:2509.26574, before applying to assess your interest in the work. You will work on research-grade problems in your own narrowly matched subfield, producing written reasoning detailed enough for another specialist to independently follow and verify. The expected standard of proof is especially rigorous.

Key Responsibilities

• Create research-level problems, solve them, review completed work, or audit work, based on the fit between your publication record and the assigned area.
• Develop complete, independently verifiable written reasoning for each assignment.

Research Areas

• Special functions, including Gaussian hypergeometric functions, parameter differentiation, quadratic transformation identities, analytic continuation in a series index, digamma-function series, and asymptotic and series expansions.
• Integrable systems, including half-wave maps, Lax pairs and isospectral flows, Hilbert transforms and singular integral operators, Haldane-Shastry spin chains, Calogero-Moser systems, conserved-charge hierarchies, solitons, and numerical quadrature of singular integrals.
• Permutation combinatorics for random tensor-network entanglement, including Cayley distance and 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, extended obstruction tensors, Schouten and Weyl curvature tensors, order-by-order 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 particularly well suited; senior PhD students with a strong first-author publication record may apply.
• Published research on at least one of the specific phenomena listed above. Broad mathematical-physics experience or method familiarity alone is insufficient without publication on the relevant phenomenon.
• Evidence in your own publications of at least one method family: special-function analysis; integrability; combinatorial methods involving symmetric groups, non-crossing partitions, Weingarten calculus, or multipartite entanglement; or geometric methods involving ambient metrics, Weyl covariance, curvature tensors, Ricci-flatness, or Poincare-Einstein expansions.
• A verifiable record of three to five representative papers, preferably from the past five years, with arXiv IDs or DOIs. First authorship is strongly preferred, and listed papers will be checked against public records.
• Working proficiency with LaTeX, Python, SymPy, and Jupyter. Familiarity with an agentic coding extension in VS Code is helpful but not required if gaps are disclosed honestly.
• English proficiency at B2 level or higher, including the ability to communicate written reasoning clearly.

Work Terms

• Remote, hourly independent-contractor engagement.
• 10 hours per week for an 8 to 10 week period, starting immediately.
• Asynchronous work with no fixed hours.
• Assignments are agreed after matching you to a research area.

Compensation

$80 to $110 per hour, determined by the depth of your subdomain match.

Application Process

• Complete the attached application form with your education, research experience, method self-attestation, and up to five research areas that best match your background.
• For every selected area, provide an arXiv ID or DOI for your own paper, your author position, and the methods demonstrated. Selections without supporting publication evidence are not scored.
• Your papers and authorship will be verified against the public record.
• Following verification, candidates may proceed directly or join a short live call to align on the research area and assignment.
• A 30 to 45 minute assessment may be requested only when needed; most applicants will not complete one.