School of Mathematical SciencesLocation: Bailrigg, Lancaster, UKSalary: £39,906 to £46,049(Full-Time/Indefinite with End Date)Closing Date: Sunday 29 November 2026Interview Date: Friday 18 December 2026Reference: 1137-26
Kontsevich introduced Calabi-Yau (CY) triangulated categories in the context of mirror symmetry, and 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.
You are expected to hold a 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. You will be expected to learn quickly, engage with new ideas, and contribute new insights.
This work will take place in our thriving Pure Mathematics section, which has considerable expertise in algebra, geometry, analysis, probability, and discrete mathematics. Lancaster is one of the UK’s top departments in Mathematical Sciences, ranked 7th in the most recent Research Excellence Framework, and joint 1st for the impact of its research. The School, which holds an Athena SWAN Bronze Award, strives to provide a supportive and friendly environment for early career researchers, and offers a comprehensive career development programme. You will be able to focus on your research as the post carries no teaching or administrative duties. Teaching experience will be available on a voluntary basis should you wish to gain teaching experience. You will be encouraged to conduct research visits and will have access to travel funds to do so.
Please note: unless specified otherwise in the advert, all advertised roles are UK based.
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