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Peter Scholze (German pronunciation: [ˈpeːtɐ ˈʃɔltsə] ⓘ; born 11 December 1987 [2]) is a German mathematician known for his work in arithmetic geometry. He has been a professor at the University of Bonn since 2012 and director at the Max Planck Institute for Mathematics since 2018.
Dustin Clausen is an American-Canadian [1] mathematician known for his contributions to algebraic K-theory and the development of condensed mathematics, in collaboration with Peter Scholze. His research interests include the intersections of number theory and homotopy theory.
Condensed mathematics is a theory developed by Dustin Clausen and Peter Scholze which replaces a topological space by a certain sheaf of sets, in order to solve some technical problems of doing homological algebra on topological groups.
A simpler proof was suggested almost at the same time by Guy Henniart, [12] and ten years later by Peter Scholze. Taylor, together with Christophe Breuil , Brian Conrad and Fred Diamond , completed the proof of the Taniyama–Shimura conjecture , by performing quite heavy technical computations in the case of additive reduction.
The following IMO participants have either received a Fields Medal, an Abel Prize, a Wolf Prize or a Clay Research Award, awards which recognise groundbreaking research in mathematics; a European Mathematical Society Prize, an award which recognizes young researchers; or one of the American Mathematical Society's awards (a Blumenthal Award in ...
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More foundational material was developed after the first book, and especially an extended theory of perfectoid rings and perfectoid spaces which generalizes the recent work of Peter Scholze. These aspects were recapitulated in the book "Foundations for Almost Ring Theory". [2]
In mathematics, especially in topology, a pyknotic set is a sheaf of sets on the site of compact Hausdorff spaces (with some fixed Grothendieck universes). The notion was introduced by Barwick and Haine to provide a convenient setting for homological algebra. [1] The term pyknotic comes from the Greek πυκνός, meaning dense, compact or ...