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Explore recent advancements in p-adic and perfect geometry through this 1-hour 4-minute lecture on meromorphic vector bundles on the Fargues-Fontaine curve. Delve into the categorical version of the local Langlands correspondence, examining two main approaches: one using p-adic geometry and the stack of vector bundles, and another employing perfect geometry and the Kottwitz stack. Investigate the introduction of a third object, the stack of meromorphic vector bundles, and its potential role in bridging the gap between the two conjectures. Gain insights into ongoing research conducted in collaboration with Alex Ivanov, as presented by Ian Gleason at the Hausdorff Center for Mathematics.
