What is a shtuka / An infinity-adic criterion of good reduction for Drinfeld modules

Preliminary (30 Mins): What is a shtuka?

Abstract:

In the literature there are many seemingly incompatible definitions of
a shtuka. I will explain the unifying idea which stands behind them.
I will also discuss applications of shtukas to Langlands program and
to the theory of Galois representations.

15mins break 
Main talk (45 mins): An infinity-adic criterion of good reduction for Drinfeld modules

Abstract:

J.-K. Yu discovered that a Drinfeld module has a p-adic Tate module not
only for every prime p of the coefficient ring, but also for the place
$p = \infty$. This contrasts with the case of abelian varieties where
a Tate module can not be a vector space over the reals.

I will explain how the construction of J.-K. Yu interacts with
Fargues-Fontaine curve, and how this leads to a good reduction criterion
of a new kind. This result supplements the classical criteria of
Néron-Ogg-Shafarevich and Grothendieck-de Jong.

No previous knowledge of abelian varieties, Drinfeld modules or
Fargues-Fontaine curve will be necessary to understand the talk.