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

• To become familiar with relevant literature on Deligne—Lusztig theory and spetses.
• 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.
• To develop new techniques to prove local-global counting conjectures (relating local and global information concentrated at a prime).
• To apply methods from fusion systems to extract local information about compact Lie and p-compact groups.
• To write research papers suitable for publication in high quality academic journals.
• To disseminate results of the project at both national and international conferences.
• To support the PI by enhancing relationships with existing collaborators and by assisting the establishment of relationships with new collaborators.
• To undertake tasks assigned by the PI.
• To participate in activities within

Key Requirements:

• Background in algebra and/or algebraic topology
• Experience of preparing and/or publishing original work as academic journal papers and/or conference papers
• Research in representation theory and/or homotopy theory and/or group theory and/or fusion systems
• Excellent written and oral communication skills
• Self-motivated with ability to meet deadlines
• Excellent interpersonal, and organisational skills
• Ability to work as part of a team and collaborate with others
• Willingness to undertake further training as required
• PhD (or near completion) in mathematics
• Commitment to observing the University’s Equal Opportunities policy at all times.

Desirable:

• Familiarity with the local-global conjectures in modular representation theory and the application of Deligne—Lusztig theory to these problems
• Acquaintance with homotopy theory, p-local analysis, Hecke algebras and/or the theory of fusion systems
• Knowledge of methods to reduce problems of representation theory to the case of simple groups
• Working in a high-quality academic research environment
• Authoring original work, in the highest quality refereed academic journals
• A strong publication track record
• Ability and willingness to teach at an undergraduate level

For more information on the role please refer to the Job Description and Person Specification.

Informal enquiries should be directed to Jason Semeraro, via email to j.p.semeraro@lboro.ac.uk or by telephone to 01509 223327

Our Benefits

At Loughborough, our benefits are designed to support your life inside and outside of work, helping you to thrive and feel valued as part of our community.  Examples of our benefits include:

Time off - generous holiday allowance, including 14 university closure days and bank holidays, with the option to buy extra through our holiday purchase scheme.

Where you work - access to a range of fantastic facilities with plenty of green space across our 523-acre East Midlands campus, plus an exciting community at our London campus on the Queen Elizabeth Olympic Park

Financial Wellbeing -competitive pay, two excellent pension schemes, and everyday savings opportunities.

Support for you and those close to you -through our range of life event leave policies as well as access to an on-site nursery at our East Midlands campus, flexible and hybrid working options.

Health and Wellbeing - discounted gym memberships and access to world-class sporting facilities, including physiotherapy, plus healthcare offers such as eyesight testing and wellbeing support.

Travel and sustainability- access to our electric vehicle and cycle-to-work schemes, as well as a variety of travel offers to support sustainable commuting.

Discover more about the full range of rewards and benefits at Loughborough University.