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Explore the concept of perfectoid pure singularities in this lecture by Karl Schwede from the 2025 Simons Collaboration on Perfection in Algebra, Geometry and Topology Annual Meeting. Learn what it means for a ring to have a pure (split) map to a perfectoid ring, drawing parallels to F-pure rings in characteristic p where the Frobenius map is pure. Discover how perfectoid pure singularities relate to log canonical singularities, with evidence showing they are equivalent in certain cases. Examine various examples and properties of these mathematical structures throughout this hour-long presentation that bridges concepts in algebra, geometry, and topology.
