Jordan Barnes
Jordan’s research interests are representation theory in positive characteristic. Their PhD research project is titled 'Representations of rational Cherednik algebras in positive characteristic'
Project Title
'Representations of rational Cherednik algebras in positive characteristic'
About
I am a final year PhD student at Newcastle University studying representation theory in positive characteristic.
Project Description
The representation theory of Cherednik algebras has strong connections to algebraic geometry, combinatorics, finite dimensional algebra, homological algebra, integrable systems, q-calculus and Lie theory.
In characteristic 0, it is an extremely active area of research. Far less is known in characteristic p, which makes it a very bountiful area for investigation. Even basic questions, such as describing characters of simple modules, have only been answered in a few cases.
My research entails calculating the simple modules of rational Cherednik algebras associated to the symmetric group over fields of positive characteristic, which I have done in a number of cases.
Education
MSci Natural Sciences, Lancaster University (2017)
During my undergraduate years I studied physics, chemistry, and maths. In my second year I studied abroad at the Iowa State University, USA. In my fourth year I worked with Dr Łukasz Grabowski on a project titled “Localisation of Noncommutative Group Rings”.
Supervisors
- Dr Martina Balagovic
- Dr Alina Vdovina
Contact
Email: j.barnes6@ncl.ac.uk