Funded PhD position in Mathematics (algebraic geometry).

Autonomous University of Madrid (Universidad Autónoma de Madrid); España; Presencial; EUR 22.000 - 26.000; Jornada completa

Descripción de la vacante

Autonomous University of Madrid (Universidad Autónoma de Madrid) invites applications for a four-year PhD position in Mathematics, focusing on algebraic geometry. The project is funded under the DUKES initiative and involves topics like birational geometry, moduli spaces, and geometric invariant theory.

Candidates may apply programming methods (Sagemath, Python, Lean) to address problems in the area. Excellent English is required; Spanish health system access is part of university benefits.

Formación

• Knowledge in algebraic geometry at Masters level.
• Experience with LaTeX for mathematical typesetting.
• Familiarity with Sagemath, Python, Magma or Lean is valued.

Conocimientos

Algebraic geometry knowledge

LaTeX typesetting

English (Excellent)

Educación

Master's degree in Mathematics (Algebraic Geometry)

Herramientas

Sagemath

Python

Magma

Lean

Descripción del empleo

Organisation/Company Autonomous University of Madrid (Universidad Autónoma de Madrid) Department Department of Mathematics, Faculty of Science Research Field Mathematics Researcher Profile First Stage Researcher (R1) Positions PhD Positions Application Deadline 30 Nov 2026 - 23:59 (Europe/Madrid) Country Spain Type of Contract Temporary Job Status Full-time Hours Per Week 37,5 Offer Starting Date 1 Jan 2027 Is the job funded through the EU Research Framework Programme? Not funded by a EU programme Is the Job related to staff position within a Research Infrastructure? No

Offer Description

4-year contract to carry out a PhD in Mathematics in the subject of algebraic geometry, working in one or more of the following topics:

• Birational geometry and classification of algebraic varieties.
• Moduli spaces of varieties, including Fano varieties.
• Geometric invariant theory (reductive and/or non-reductive).
• K-stability and existence of canonical metrics.
• Special holonomy, exceptional geometry, and torsion.
• Dualities, higher geometry, and vertex algebras.
• Hitchin systems, Langlands duality and mirror symmetry.

For those candidates interested, there is a possibility of applying programming techniques in different algebra and formal systems (e.g. Sagemath, Python, Lean) to solve some of these problems.

The researcher will be funded by the national project DUKES (Dualities, K-stability and special holonomy), led by Mario Garcia-Fernandez and Jesus Martinez-Garcia, based at Universidad Autónoma de Madrid (UAM) and the Institute of Mathematical Sciences (ICMAT), both in the Campus of Cantoblanco. DUKES is part of the national coordinated project GEMS (Geometric structures, moduli spaces, and dualities), comprising over 40 researchers in Spain and abroad. DUKES is funded by the Ministerio de Ciencia, Innovación y Universidades of Spain with grant number PID2025-174260NB-C21.

Specific Requirements

• Knowledge in algebraic geometry at Masters level.
• While not required, we will value subject knowledge in relation to one or more of the following topics: birational geometry, geometric invariant theory, algebraic groups, algebraic curves, algebraic surfaces, complex geometry, Fano varieties, moduli spaces, K-stability, Special holonomy, Hitchin systems and mirror symmetry.
• Experience writing and typesetting mathematics (e.g. Latex)
• While not required, we will value any experience in algebra and/or formal verification programming languages (e.g. Sagemath, Python, Magma, Lean…)

Languages ENGLISH Level Excellent

Additional Information

• 2,121.34 € gross monthly salary for the duration of the contract.
• 7,000 € research support towards research stays abroad and PhD enrollment fees (which are currently listed at around 2,000 € for the duration of the PhD studies) of at least one month of duration.
• Should the successful candidate finish their PhD before the end of the 4 year contract, this could be extended as part of an additional Postdoctoral Orientation Period (POP) for up to 12 months, not exceeding in total (PhD+POP) the full 4 years.
• The successful candidate will be an employee of the university and, as such, they will be entitled to the standard benefits of university employees, including access to the free universal Spanish health system, severance payment at the end of the contract, public pension accrual, and parental and/or maternity leave benefits, in accordance with Spanish laws and collective labour agreements.

Additional comments

The project DUKES is an equal-opportunities research group. We actively encourage applications from women and under-represented groups.