Explicit Examples of Categorical Local Langlands

Explore the intricacies of categorical local Langlands through explicit examples in this 1-hour 16-minute lecture by Eugen Hellmann from the Hausdorff Center for Mathematics. Delve into the relationship between the derived category of smooth representations of p-adic reductive groups and the derived category of coherent sheaves on the stack of corresponding L-parameters. Focus on the groups GL_2 and SL_2, examining the construction of fully faithful functors between these categories. Analyze the explicit computation of sheaf complexes associated with smooth representations, and investigate how parabolic induction, Bernstein block decomposition, and the Langlands classification of irreducible representations fit into this framework.