Representation theory of P-adic Groups

One of the most celebrated mathematical results of the last century was the Taylor-Wiles proof of Fermat's Last Theorem. Essentially, they proved a relation between modular forms and elliptic curves which was conjectured by Taniyama and Shimura and was the last missing piece for a proof of Fermat's longstanding conjecture. This correspondence is a special case of a much bigger picture, the so called Langlands Program, which conjecturally relates automorphic forms and Galois representations. One part of this program is the local Langlands conjecture which for GL(n) was proven in 2000. Emerton and Helm later extended this conjectures to families of representations of GL(n) which was recently resolved by Helm and Moss.

An important step of their proof was the theory of gamma factors in families for GL(n) which was developed by Moss. In my PhD thesis I will try to construct such gamma factors in families for representations of more general classical groups. This might help to prove the local Langlands conjecture in families for classical groups.