In a Betti/topological setting, applying categorical and 2-categorical traces to a Hecke action yields universal shtukas, excursion operators, and an S=T identity.
Categorical proof of Holomorphic Atiyah-Bott formula
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abstract
Given a symmetric monoidal $(\infty,2)$-category $\mathscr E$ we promote the trace construction to a functor. We then apply this formalism to the case when $\mathscr{E}$ is the $(\infty,2)$-category of $k$-linear presentable categories which in combination of various calculations in the setting of derived algebraic geometry gives a categorical proof of the classical Atiyah-Bott formula (also known as the Holomorphic Lefschetz fixed point formula).
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2019 1verdicts
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A toy model for the Drinfeld-Lafforgue shtuka construction
In a Betti/topological setting, applying categorical and 2-categorical traces to a Hecke action yields universal shtukas, excursion operators, and an S=T identity.