Senior Research Associate

The School of Mathematical Sciences at Lancaster University invites applications for a three-year postdoctoral position to work on the project "Mutations and geometric models". The Principal Investigator is Dr Coelho Simões and the project is funded by the Engineering and Physical Sciences Research Council (EPSRC).

Kontsevich introduced Calabi-Yau (CY) triangulated categories in the context of mirror symmetry, and they have since become ubiquitous in mathematics, particularly in geometry and representation theory. Due to their physical origin, n-CY categories have been extensively studied for n=2,3. However, as a homological condition, the n-CY property can be studied for any integer n. This means there are many more examples of n-CY categories than those of physical origin. Many categories naturally arising in modular representation theory, singularity theory, Fuss-Catalan combinatorics, and higher homological algebra are n-CY for n different from 2 and 3. The systematic study of CY categories in these wider contexts is in its infancy and many aspects remain poorly understood. The main aim of the project seeks to provide methods to address this shortfall using mutations and geometric models.

Candidates with a strong track record in one of the fields of homological algebra, representation theory or algebraic combinatorics are encouraged to apply.

Requirements:
- PhD degree in mathematics or a related discipline, with specialism in one of the fields of homological algebra, representation theory or algebraic combinatorics.
- Expertise in triangulated categories, representation theory of finite-dimensional algebras, combinatorial/geometric models arising from surfaces, singularity theory or modular representation theory is highly desirable.
- Ability to learn quickly, engage with new ideas, and contribute new insights.

The post carries no teaching or administrative duties, allowing you to focus fully on research. Teaching experience will be available on a voluntary basis. You will be encouraged to conduct research visits and will have access to travel funds.

This work will take place in the thriving Pure Mathematics section of the School, which has considerable expertise in algebra, geometry, analysis, probability, and discrete mathematics. Lancaster is ranked 7th in the most recent Research Excellence Framework and joint 1st for the impact of its research. The School holds an Athena SWAN Bronze Award and strives to provide a supportive and friendly environment for early career researchers, offering a comprehensive career development programme.

The position starts on 1st February 2027 (or as soon as possible after), for up to 36 months.

When applying, candidates should attach a full CV, a cover letter, a 1-page research statement describing how your expertise is relevant to this position and your future research plans, and the details of two referees. Interviews will take place in December and will be conducted online.