Job description
Full Time, Fixed Term.
Loughborough University is seeking to appoint a Postdoctoral Research Associate in the areas of Algebra and Geometry to conduct research under the direction of Dr Jason Semeraro on an EPSRC funded project “Exotic Representation Theory”. The aim of the project is understand how recent state-of-the-art advances in homotopy theory (related to fixed points of classifying spaces) can be applied to study the local-global conjectures of modular representation theory. The project will last for up to 6 months and will be carried out jointly by the RA and Dr Jason Semeraro as the Supervisor / Principal Investigator (PI).
Job Grade: Specialist and Supporting Academic Grade 6
Job Purpose
To conduct research in algebra and geometry; in particular generalisation of Deligne—Lusztig theory to the setting of spetses by applying methods from homotopy theory. To develop new techniques to tackle local-global conjectures in modular representation theory using fusion systems. To investigate the relationship between Hecke algebras and blocks of unipotent groups.
Job Duties
1. To become familiar with relevant literature on Deligne—Lusztig theory and spetses.
2. To learn and apply relevant homotopy-theoretic techniques such as constructing classifying spaces, decomposing spaces as homotopy colimits and taking fixed points under unstable Adams operators.
3. To develop new techniques to prove local-global counting conjectures (relating local and global information concentrated at a prime).
4. To apply methods from fusion systems to extract local information about compact Lie and p-compact groups.
5. To write research papers suitable for publication in high quality academic journals.
6. To disseminate results of the project at both national and international conferences.
7. To support the PI by enhancing relationships with existing collaborators and by assisting the establishment of relationships with new collaborators.
8. To undertake tasks assigned by the PI.
9. To participate in activities within
Key Requirements:
10. Background in algebra and/or algebraic topology
11. Experience of preparing and/or publishing original work as academic journal papers and/or conference papers
12. Research in representation theory and/or homotopy theory and/or group theory and/or fusion systems
13. Excellent written and oral communication skills
14. Self-motivated with ability to meet deadlines
15. Excellent interpersonal, and organisational skills
16. Ability to work as part of a team and collaborate with others
17. Willingness to undertake further training as required
18. PhD (or near completion) in mathematics
19. Commitment to observing the University’s Equal Opportunities policy at all times.
Desirable:
20. Familiarity with the local-global conjectures in modular representation theory and the application of Deligne—Lusztig theory to these problems
21. Acquaintance with homotopy theory, p-local analysis, Hecke algebras and/or the theory of fusion systems
22. Knowledge of methods to reduce problems of representation theory to the case of simple groups
23. Working in a high-quality academic research environment
24. Authoring original work, in the highest quality refereed academic journals
25. A strong publication track record
26. Ability and willingness to teach at an undergraduate level
For more information on the role please refer to the