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Representations of p-adic groups and dg-algebras (STEVENSS_U21SCIOM)

School of Mathematics

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Prof S Stevens , Dr V Miemietz No more applications being accepted Competition Funded PhD Project (Students Worldwide)
Norwich United Kingdom Pure Mathematics

About the Project

The representation theory of p-adic groups has been a highly active area of research over the last fifty years, motivated by the Local Langlands Conjectures and its deep connections to Number Theory. To begin with, only representations with complex coefficients were considered but, more recently, representations with coefficients in other rings or fields have been studied also. In particular, when the field has characteristic p (the same p), the situation changes quite drastically and adapting the previous theory only yields a part of the picture. 

The purpose of this project is to use techniques from higher representation theory to understand the missing parts. A major tool in the complex case is to translate questions about representations of a p-adic group into questions about certain algebras, called Hecke algebras. These can be enhanced to a dg Hecke algebra which contains much more structural information, even in the case of complex representations. The project would study this, starting with small examples for complex representations, before moving on to the characteristic p case. The ultimate aim would be to interpret this in terms of higher representation theory, as the 2-morphisms in a 2-category.  

The successful applicant will join a very active and supportive group in Representation Theory at UEA (currently comprising 4 faculty, 2 postdocs and 4 PhD students), and will be co-supervised by Shaun Stevens and Vanessa Miemietz. 

For more information on the supervisor for this project, please go here  

This is a PhD programme. The start date is 1st October 2021. The mode of study is full time. The studentship length is 3 years. 

Entry requirements: 2:1 in Mathematics

Funding Notes

Successful Home candidates who meet UKRI’s eligibility criteria will be awarded an EPSRC studentship in Mathematical Sciences covering fees, stipend (£15,285 pa) for 4 years. The eligibility requirements are detailed in UKRI Training Grant Guidance: (see Annex B for criteria for classification as a Home student).

Applicants to this project will also be considered for a 3 year UEA funded studentship covering stipend (£15,285 pa), tuition fees (Home only). International applicants (EU/non-EU) are eligible for UEA funded studentships but required to fund the difference between Home and International tuition fees (which are detailed on the University’s fees pages
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