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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.
Six-Functor Formalisms, lecture notes for course WS 22/23. Condensed Mathematics and Complex Geometry, lecture notes for course SS 22. Geometrization of the local Langlands correspondence, lecture notes and videos. Lectures on Analytic Geometry, lecture notes for course WS 19/20. Lectures on Condensed Mathematics, lecture notes for course SS 19.
- Root Harvest
- Numbers from Shapes
- Scholze’S Tour de Force
- Have Curve, Will Travel
- A Local Correspondence
- Foundation Building
- The End of The Beginning
The Langlands program is a sprawling research vision that begins with a simple concern: finding solutions to polynomial equations like x2 − 2 = 0 and x4 − 10x2 + 22 = 0. Solving them means finding the “roots” of the polynomial — the values of x that make the polynomial equal zero (x = ±2–√ for the first example, and x = ±5±3–√−−−−−−√for the second)...
Beginning in the early 1980s Vladimir Drinfeld(opens a new tab) and later Alexander Beilinson(opens a new tab)proposed that there should be a way to interpret Langlands’ conjectures in geometric terms. The translation between numbers and geometry is often difficult, but when it works it can crack problems wide open. To take just one example, a basi...
In September 2014, Scholze was teaching a special course at the University of California, Berkeley. Despite being only 26, he was already a legend in the mathematics world. Two years earlier he had completed his dissertation, in which he articulated a new geometric theory based on objects he’d invented called perfectoid spaces. He then used this fr...
At the same time Scholze was giving his lectures, Fargues was attending a special semester at the Mathematical Sciences Research Institute(opens a new tab) just up the hill from the Berkeley campus. He had thought a lot about the p-adic numbers, too. For the past decade he’d worked with Jean-Marc Fontaine in an area of math called p-adic Hodge theo...
The original Langlands conjectures are about matching representations of the Galois groups of the rational numbers with automorphic forms. The p-adics are a different number system, and there is a version of the Langlands conjectures there, too. (Both are still separate from the geometric Langlands program.) It also involves a kind of matching, tho...
Following their time together in Berkeley, Fargues and Scholze spent the next seven years establishing a geometric theory that would allow them to reconstruct the Fargues-Fontaine curve in a form suitable for their plans. “In 2014 it was basically already clear what the picture should be and how everything should fit together. It was just that ever...
Specifically, they came up with two different kinds: Coherent sheaves correspond to representations of p-adic groups, and étale sheaves to representations of Galois groups. In their new paper, Fargues and Scholze prove that there’s always a way to match a coherent sheaf with an étale sheaf, and as a result there’s always a way to match a representa...
Jul 28, 2021 · It establishes that an area of math called real functional analysis still works if you replace topological spaces with condensed sets. Scholze began the proof on a Monday. He worked entirely in his head, barely writing anything down, let alone using a computer.
Aug 1, 2018 · By constructing a perfectoid version of hyperbolic three-space, Scholze has discovered an entirely new suite of reciprocity laws. “Peter’s work has really completely transformed what can be done, what we have access to,” Caraiani said.
Jun 18, 2021 · Peter Scholze wants to rebuild much of modern mathematics, starting from one of its cornerstones. Now, he has received validation for a proof at the heart of his quest from an unlikely source:...
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Prof. Dr. Peter Scholze. Homepage am MPIM. Arbeitsgruppe Arithmetische Geometrie und Darstellungstheorie in Bonn. Zuletzt geändert: September 2022, Peter Scholze.
