About the Project
One of the difficulties in studying this is that the representations of G are (almost all) infinite-dimensional, so they are quite hard to get a handle on. One way for doing so, which has been very successful, is to restrict them to compact open subgroups K: we then look for representations of K whose presence in this restriction characterizes some property which representations of G might have; this property might be being “unramified”, ”tame”, “generic”,… Similarly, this restriction can be used to give very explicit descriptions of the representations of G, using arithmetic data. Such results also have interpretations via the Langlands correspondence, so consequences for the absolute galois group.
This PhD project will be in the area of the local Langlands correspondence, exploring some of the problems raised above, or related questions.
Project supervisor: https://people.uea.ac.uk/shaun_stevens
Mode of study: Full time
Start date: October 2020
Entry requirements: First degree (2:1 or above) in Mathematics.
A bench fee is also payable on top of the tuition fee to cover specialist equipment or laboratory costs required for the research. Applicants should contact the primary supervisor for further information about the fee associated with the project.
"Représentations l-modulaires d'un groupe réductif p-adique avec l≠p," Marie-France Vignéras, Progress in Mathematics, 137, Birkhäuser Boston, Inc., Boston, MA, 1996.
“Eisenstein series and automorphic L-functions,” Freydoon Shahidi, American Mathematical Society Colloquium Publications, 58. American Mathematical Society, Providence, RI, 2010.
“The supercuspidal representations of p-adic classical groups,” Shaun Stevens, Invent. Math. 172(2) (2008) 289-352.
“Jordan blocks of cuspidal representations of symplectic groups,” Corinne Blondel, Guy Henniart and Shaun Stevens, Algebra Number Theory 12 (2018), no. 10, 2327–2386.
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