Research output per year
Research output per year
Dr
My research revolves around the preresentation theory of the finite W-algebras. These are mysterious new objects which exist on the boundary between the zero characteristic and positive characteristic realms of Lie theory. To be precise, there are ordinary and modular versions which are closely related. The ordinary cases seem to control certain geormetric properties of representations of complex semisimple Lie algebras, whilst the modular specimens should be seen as the fundamental unit of currency when investigating representations of reduced enveloping algberas of restricted Lie algebras (spooky eh?). My past research has linked the characteristic zero finite W-algebra theory with primitive ideals in enveloping algebras, whilst my future research shall attempt to strengthen the connections between the ordinary and modular realms.
People: I took my PhD with Sasha Premet at the University of Manchester where he taught me the joys of modular Lie theory. After that I spent a year at the University of East Anglia working with Vanessa Miemietz where, amongst other things, we studied Chriss and Ginzburg's book 'Complex Geometry and Representation Theory' - a wonderful read, if somewhat terse. Now I'm taking a short stint in York working with Maxim Nazarov.
NB: if you google Maxim Nazarov you'll find:i) a high powered professor working with Yangians; ii) a Russian underwear model. My supervisor is the former, not the latter.
Erdős-Bacon Number: The Erdos number, e(m), of a mathematician, m, counts the distance of that mathematician from Paul Erdős on the collaboration graph. The Bacon number, b(a), counts the distance of an actor from Kevin Bacon on the coappearance graph (two actors are said to coappear if they have acted in the same film). If m = a then we may define the Erdős-Bacon number to be E(m) = e(m) + b(m). Having done extensive research I have found that E(Lewis) < 9. The inequality b(Lewis) < 4 actually follows from the fact that I was once an extra in a film being shot in my village. I'm not totally sure that counts. If there are any experts in Bacon numbers reading this then I'd be grateful for clarrification on that matter. By life's ambition is to obtain a finite Erdős-Bacon-Sabbath number.
Research output: Contribution to journal › Article › peer-review
Research output: Contribution to journal › Article › peer-review
Research output: Thesis › Doctoral Thesis