Peter Scholze

Peter Scholze
George Bergman · CC BY-SA 4.0 · source
Name	Peter Scholze
Birth date	1987
Birth place	Dresden
Nationality	German
Fields	Mathematics
Workplaces	University of Bonn, University of Cambridge, Institute for Advanced Study
Alma mater	University of Bonn
Known for	Perfectoid spaces, p-adic Hodge theory
Awards	Fields Medal, Gottfried Wilhelm Leibniz Prize

Peter Scholze Peter Scholze is a German mathematician noted for work in algebraic geometry, number theory, and arithmetic geometry. He gained prominence for introducing techniques that connect p-adic Hodge theory with homotopy-theoretic and geometric methods, influencing research at institutions such as the Institute for Advanced Study and the University of Bonn. His work has been recognized by major prizes from organizations including the International Mathematical Union and the Deutsche Forschungsgemeinschaft.

Early life and education

Scholze was born in Dresden and completed secondary studies in Germany before attending the University of Bonn, where he studied under advisors including Bürkard F. Bams? and later worked with figures connected to Gerd Faltings, Jean-Marc Fontaine, and Kiran Kedlaya. During his doctorate at the University of Bonn he developed ideas that would later crystallize into concepts resonating with work by Alexander Grothendieck, Jean-Pierre Serre, Pierre Deligne, and Barry Mazur. Early influences included seminars and collaborations at institutions such as the Max Planck Institute for Mathematics, the Hausdorff Center for Mathematics, and interactions with scholars linked to Princeton University and the Mathematical Sciences Research Institute.

Mathematical work and contributions

Scholze introduced the notion of perfectoid spaces, building on foundational concepts from Tate, Fontaine, and techniques related to Hodge theory developed by Phillip Griffiths and Claire Voisin. His perfectoid framework created new bridges between p-adic geometry and comparative approaches in motivic cohomology, echoing themes from Grothendieck's work and connecting to advances by Bhargav Bhatt, Matthew Morrow, and Kiran Kedlaya. Scholze's contributions impacted the proof strategies for cases of the Local Langlands correspondence, engaging with research by Michael Harris, Richard Taylor, and Laurent Fargues. He developed new period maps and comparison theorems in p-adic Hodge theory that influenced subsequent results by Peter L. Taylor? and collaborators at the Institute Henri Poincaré and Courant Institute. His methods have been used in work related to the Langlands program, intersecting with results of Robert Langlands, Edward Frenkel, and groups collaborating at the Perimeter Institute.

Academic career and positions

After earning his doctorate at the University of Bonn, Scholze held positions including professor at the University of Bonn and positions at the Institute for Advanced Study in Princeton, New Jersey. He has participated in programs at the Clay Mathematics Institute, the Mathematical Sciences Research Institute, and delivered lectures at venues such as IHES, Harvard University, Stanford University, and the University of Cambridge. Scholze has supervised doctoral students who continued research in areas overlapping with work by Kiran Kedlaya, Bhargav Bhatt, and researchers associated with ETH Zurich and the University of Chicago. He has served on editorial boards and committees linked to the European Research Council and collaborated with groups at the Max Planck Institute for Mathematics and the Simons Foundation.

Awards and recognitions

Scholze received the Fields Medal and the Gottfried Wilhelm Leibniz Prize, among other honors. He was awarded prizes from the European Mathematical Society, the London Mathematical Society, and national awards administered by the Deutsche Forschungsgemeinschaft. His named lectures and invited addresses include symposium talks at the International Congress of Mathematicians, plenary engagements at the European Congress of Mathematics, and distinguished lectures at Princeton University and Cambridge University. Scholze's work has been cited in prize citations alongside contributions by Gerd Faltings, Jean-Pierre Serre, and Pierre Deligne.

Selected publications and lectures

- "Perfectoid spaces" — foundational publication introducing perfectoid spaces, influencing developments connected to work by Jean-Marc Fontaine, Alexander Grothendieck, and Jean-Pierre Serre. - Papers on p-adic Hodge theory and comparison isomorphisms that built on techniques from Tate and Barry Mazur. - Lectures at the International Congress of Mathematicians, seminars at the Institute for Advanced Study, and series at the Hausdorff Center for Mathematics and MSRI. - Collaborative works with researchers in the networks of Bhargav Bhatt, Kiran Kedlaya, Laurent Fargues, and others active at the European Research Council-funded projects.

Category:German mathematicians Category:Fields Medalists Category:University of Bonn faculty