Mathematics PhD Researcher (STEM ) $20 – $50/hr Remote India

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Role Overview

Algebraic Geometry

Large Language Models (LLMs)

Key Responsibilities

• Assess the accuracy, rigor, and conceptual depth of LLM-generated outputs in areas such as:
• Schemes, sheaves, and cohomology
• Algebraic curves, varieties, and stacks
• Class field theory, Galois representations, and modular forms
• Local/global fields, arithmetic geometry, and Diophantine equations
• Design mathematically rigorous tasks to test the model’s handling of advanced formal arguments and abstraction.
• Deliver detailed, structured feedback on correctness, clarity, and depth of model responses.
• Identify reasoning gaps and contribute to improvements in symbolic and abstract mathematical reasoning.
• Assist in developing evaluation protocols and benchmark datasets relevant to algebraic and arithmetic geometry.

Qualifications

• PhD or active PhD candidacy in Pure Mathematics, with a focus on:
• Algebraic Geometry
• Algebraic Number Theory
• Or a closely related field
• Expertise in foundational and advanced topics such as:
• Étale and flat cohomology, derived functors, stacks
• Valuation theory, adeles/ideles, arithmetic schemes
• Representation theory, modularity, and class field theory
• Diophantine equations and proof-based problem solving
• High precision in reading and writing formal mathematical proofs.
• Strong ability to critique abstract reasoning and logical structure.
• Excellent technical writing skills, especially in an academic or formal setting.
• Comfort working independently and asynchronously in a remote setup.

Work Arrangement

• Part-time (10–20 hours/week)
• Fully remote and asynchronous
• Contractor role via Mercor
• Weekly payments via Stripe Connect

Compensation

• Hourly rate: $20–$50, based on expertise and specialization