Sean Cotner (University of Bonn): On the Fargues-Scholze local Langlands correspondence for Yu’s supercuspidals

There are several different approaches to the local Langlands
correspondence, which can be roughly grouped as “classical”, “explicit”,
and “geometric”. Each of these has its own useful features, and it is
expected that they all ultimately yield the same correspondence, but this
is far from clear. There has been a lot of work by many people comparing
the classical and geometric approaches, and some partial work comparing
the other two pairs of approaches. I will discuss recent joint work with
Tony Feng which is focused on comparing the explicit and geometric
approaches due to Kaletha and Fargues–Scholze, respectively. Roughly, we
proceed by induction on the semisimple rank to reduce to the case of tori,
where the two approaches are known to agree. The main recent tools making
this argument possible are Feng’s modular functoriality and Scholze’s
independence of \ell.

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