Mathematical Institute of the University of Bonn

Lecture series on "Recent progress around the categorical Langlands conjecture"

Speakers: David Hansen, National University of Singapore, and Lucas Mann, Universität Münster

Monday, 16.12, 13:00 Lipschitzsaal

Wednesday, 18.12, 13:00, Lipschitzsaal

Friday, 20.12, 14:05, MPI Main Lecture Hall

Subtitle for lectures 1/2: A strategy for categorical local Langlands

Abstract 1: We will quickly review the statement of categorical local Langlands, and explain a strategy of proof for "well-understood groups", which notably includes GLn. We will try to highlight both the similarities and differences from the recent proof of geometric Langlands.

Abstract 2: We will explain some of the key new intermediate results and technical ingredients in this project: duality theorems for the spectral action; the spectral geometric lemma; the spectral temperization theorem.

Subtitle for lecture 3: Fargues's conjecture, 10 years on
Abstract 3: In December 2014, Fargues gave a seminal lecture at MSRI, introducing his revolutionary idea that local Langlands should amount to geometric Langlands on the Fargues-Fontaine curve. Already in this talk, he conjectured the existence of certain Hecke eigensheaves associated with discrete L-parameters, and predicted some of their properties. In the subsequent 10 years, Fargues's vision has developed into a very wide-ranging and fruitful program which is now on solid technical footing.

Taking advantage of these developments, we will return to Fargues's original setting and formulate an extremely precise refinement of Fargues's eigensheaf conjecture for a very general class of L-parameters, and discuss what is known about it. We will also formulate the so-called magic wand conjecture.