Seminar of Algebra

Back to main page.

Local Langlands in families for classical groups in the banal case

Speaker:
Robert Kurinczuk (University of Sheffield)
Email:
robkurinczuk@gmail.com
Location:
Seminario I del IMUS
Date:
Wed, 29 oct 2025 10:00
I completed my PhD in 2012 under the supervision of Professor Shaun Stevens at the University of East Anglia, where I studied infinite dimensional symmetries in a branch of Algebra called Representation Theory. Following on from this, I held postdoctoral fellowships, first at the University of Bristol then at Imperial College London, before joining University of Sheffield in 2021.

The conjectural local Langlands correspondence connects representations of p-adic groups to representations of Galois groups of local fields called Langlands parameters. In joint work with Dat, Helm, and Moss, we have constructed moduli spaces of Langlands parameters over Z[1/p] and studied their geometry. We expect this geometry is reflected in the representation theory of the p-adic group. In the quasi-split case, our main conjecture "local Langlands in families" describes the GIT quotient of the moduli space of Langlands parameters in terms of the endomorphisms of a particular representation, a Gelfand-Graev representation, generalising a theorem of Helm-Moss for GL(n). I will explain how after inverting the "non-banal primes" for our group we can prove this conjecture for the local Langlands correspondence for classical groups of Arthur, Mok, Atobe-Gan-Ichino-Kaletha-Minguez-Shin, and others.