Peter Scholze

Peter Scholze (2014)

Peter Scholze (born December 11, 1987 in Dresden ) is a German mathematician and recipient of the Fields Medal . He is a professor at the Rheinische Friedrich-Wilhelms-Universität Bonn and director at the Max Planck Institute for Mathematics . His field of work lies at the intersection of number theory and algebraic geometry .

Life

Peter Scholze was born on December 11, 1987 in Dresden. His father is a physicist, his mother a computer scientist. He grew up in Berlin and attended the Heinrich-Hertz-Gymnasium in Berlin-Friedrichshain , which was characterized by a mathematical profile . At the International Mathematical Olympiads , he won three golds and one silver. From the age of sixteen he was supported by Professor Klaus Altmann at the Free University of Berlin . After a short time he also took part in mathematics seminars at the university. From the age of eighteen he was supported by Michael Rapoport , professor of arithmetic algebraic geometry at the Rheinische Friedrich-Wilhelms-Universität Bonn .

After his graduation in 2007 he studied on a scholarship from the studienstiftung mathematics at the University of Bonn, where he developed the Bachelor's degree in three semesters and the Master's degree completed in two semesters and 2012 with a dissertation entitled Perfectoid Spaces at Michael Rapoport received his PhD. From July 2011 until the end of June 2016, he spent five years as a Fellow of the Clay Mathematics Institute in Cambridge ( Massachusetts ).

In the 2012/2013 winter semester, Scholze was appointed to one of the Hausdorff mathematics professorships at the Cluster of Excellence in Bonn. His specialty is arithmetic-algebraic geometry as part of the Langlands program . Due to his extraordinary achievements in the master's and doctoral theses, he did not go through a habilitation process . His inaugural lecture was on numbers and geometry.

He is married to a mathematician and has one daughter.

Scientific contributions

As a 22-year-old student, Scholze provided new evidence of Langlands' local correspondence , first proven in 2000 by Guy Henniart , Michael Harris and Richard Taylor . He was able to greatly simplify this complex and extensive proof. In his dissertation he introduced the new technique of perfectoid spaces , which allows to switch between bodies with mixed characteristics and those with positive characteristics in number-theoretical questions . The technique generalizes a sentence by Jean-Pierre Wintenberger and Jean-Marc Fontaine (1979) and uses the construction of adic spaces according to Roland Huber . One application is a more general formulation of Gerd Faltings' Almost Purity Theorem in the p-adic Hodge theory . Furthermore, this technique enables a geometric interpretation for other problems, for example with Shimura varieties and Rapoport- zinc spaces . Michael Harris , who teaches at Columbia University and is an expert in arithmetic geometry , assessed Scholze's concept formation of perfectoid spaces as follows: "In contemporary mathematics there is seldom such a clear example of a new concept formation."

In 2018, Scholze and Jakob Stix found what they considered to be an unrecoverable gap in the proof of the abc conjecture by Shin'ichi Mochizuki presented in 2012 . Mochizuki himself sees himself misunderstood and insists on the correctness of his evidence.

Awards

2013:

• SASTRA Ramanujan Prize
• Prix ​​Peccot

2014:

• Clay Research Award together with Maryam Mirzakhani
• Invited Speaker at the ICM in Seoul (Perfectoid spaces and their applications)

2015:

• Cole Prize of the American Mathematical Society in the field of algebra for "his work on perfectoid spaces, which led to the solution of an important special case of Deligne 's 'weight monodromy conjecture' " (from the laudation )
• Ostrowski Prize
• Fermat price

2016:

• One of the three New Horizons in Mathematics Awards was intended for him, which are intended for young scientists, are funded by a few US entrepreneurs and are endowed with 100,000 dollars each. Scholze refused to accept this award in November 2015.
• Gottfried Wilhelm Leibniz Prize
• Academy Award of the Berlin-Brandenburg Academy of Sciences
• EMS price
• Plenary lecture at the European Congress of Mathematicians in Berlin (Perfectoid spaces and their applications)

2017:

• Elected member of the Leopoldina
• Admission to the Academy of Sciences and Literature (AdW-Mainz)
• Admission to the Berlin-Brandenburg Academy of Sciences

2018:

• Elected to the North Rhine-Westphalian Academy of Sciences and Arts and appointment as one of the directors of the Max Planck Institute for Mathematics
• For the International Congress of Mathematicians 2018 in Rio de Janeiro , Scholze was selected for a plenary lecture (p-adic geometry). There he received the Fields Medal for the “revolution in arithmetic algebraic geometry over p-adic bodies through the introduction of perfectoid spaces with application to Galois representations and for the development of new cohomology theories” . Peter Scholze received this as the second German after Gerd Faltings . Both research in the field of algebraic number theory and are currently directors at the Max Planck Institute for Mathematics in Bonn.

2019:

• Order of Merit of the Federal Republic of Germany

Fonts (selection)

• Perfectoid Spaces. (PDF; 571 kB), dissertation, Bonn 2011.
• Perfectoid spaces. In: Publications mathématiques de l ' Institut des Hautes Études Scientifiques . 116 (2012), No. 1, pp. 245-313.
• Perfectoid Spaces: A survey. In: Proceedings of the International Conference on current developments in mathematics. 2012.
• The Langlands-Kottwitz method and deformation spaces of p-divisible groups. In: Journal of the American Mathematical Society . 26 (1), 2013, pp. 227-259.
• With Sug Woo Shin: On the cohomology of compact unitary group Shimura varieties at ramified split places. In: Journal of the American Mathematical Society. 26 (1), 2013, pp. 261-294, Arxiv.
• p-adic Hodge theory for rigid-analytic varieties. In: Forum of Mathematics, Pi. 1, e1, 2013.
• The Langlands-Kottwitz approach for some simple Shimura varieties. In: Inventiones Mathematicae. 192, 2013, pp. 627-661, Arxiv.
• The Local Langlands Correspondence for GL _n over p-adic fields. In: Inventiones Mathematicae. 192, 2013, pp. 663-715. Arxiv.
• Perfectoid spaces and their applications. In: Proceedings of the International Congress of Mathematicians (ICM) . 2014.
• On torsion in the cohomology of locally symmetric varieties. In: Annals of Mathematics . Volume 182, 2015, pp. 945-1066, Arxiv.
• With Bhargav Bhatt: The pro-étale topology for schemes. In: Astérisque. 369 (2015), 99-201.
• With Bhargav Bhatt: Projectivity of the Witt vector affine Grassmannian. In: Inventiones Mathematicae. 209 (2017), No. 2, pp. 329-423.
• With Ana Caraiani : On the generic part of the cohomology of compact unitary Shimura varieties. (PDF; 813 kB), In: Annals of Mathematics. Volume 186, 2017, pp. 649-766.
• p-adic geometry. In: Proceedings of the ICM. 2018.
• with P. Allen, A. Caraiani, Frank Calegari , Toby Gee , D. Helm, B. Le Hung, J. Newton, R. Taylor , Jack Thorne : Potential automorphy over CM fields , Arxiv 2018

literature

• Manfred Dworschak: Mozart of mathematics . In: Der Spiegel . No. 31 , 2018, p. 94-96 ( online ).

Web links

Commons : Peter Scholze  - Collection of images, videos and audio files

• Literature by and about Peter Scholze in the catalog of the German National Library
• Homepage at the University of Bonn
• Employee information on Peter Scholze at the University of Bonn
• Interview with Research Fellow Peter Scholze , Clay Mathematics Institute , 2012
• Peter Scholze - the mathematical clairvoyant , Spektrum.de, August 1, 2018
• Erica Klarreich: The Oracle of Arithmetic , Quanta Magazine, June 28, 2016
• Videos by and about Peter Scholze in the AV portal of the Technical Information Library
• Michael Hesse: Interview with Peter Scholze: "Mathematicians need a high tolerance for frustration" , Berliner Zeitung , August 16, 2018

Individual evidence

1. ↑ Peter Scholze. In: uni-bonn.de. Hausdorff Center for Mathematics at the University of Bonn , April 26, 2017, accessed on April 1, 2020 . 
2. ↑ Peter Scholze. In: dnb.de. Catalog of the German National Library, accessed on April 1, 2020 . 
3. ↑ Jens Thomas: You can count on him. In: tagesspiegel.de. August 3, 2005, accessed April 1, 2020 . 
4. ↑ Peter Scholze. In: IMO-official.org. International Mathematical Olympiad (IMO), accessed April 1, 2020 . 
5. ↑ ^{a b} Holger Dambeck: Professor about Peter Scholze as a student: "I've never seen someone like that". In: Spiegel.de. August 1, 2018, accessed April 1, 2020 . 
6. ↑ ^{a b} Christoph Drösser: Fields Medal 2018 goes to 30-year-old German: Perfectoid! Peter Scholze receives the "Maths Nobel Prize". In: swr.de . August 1, 2018, archived from the original on August 2, 2018 ; accessed on August 9, 2018 . 
7. ^ Mathematics lessons at the Heinrich-Hertz-Gymnasium. Aims. In: hhgym.de. Heinrich-Hertz-Gymnasium, accessed on April 1, 2020 . 
8. ↑ German National Academic Foundation: Annual Report 2017, p. 81.
9. ↑ ^{a b} Peter Scholze in the Mathematics Genealogy Project (English)
10. ↑ Peter Scholze. Short résumé. In: claymath.org. Clay Institute, accessed April 1, 2020 . 
11. ↑ Peter Scholze: Perfectoid spaces . Ed .: University and State Library Bonn. Bonn 2012 ( uni-bonn.de [accessed April 1, 2020]).
12. ^ Mathematician Peter Scholze (24) accepts the offer to Bonn - as the youngest German W3 professor. In: idw-online.de. October 15, 2012, accessed April 1, 2020 . 
13. ↑ Only 24 years old. This is Germany's youngest math professor. In: tz-online.de. October 15, 2012, accessed April 1, 2020 . 
14. ^ Fields Medal for Peter Scholze. Bonn math professor honored with high distinction. In: rp-online.de . August 1, 2018, accessed April 1, 2020 . 
15. ↑ Numbers and Geometry. Inaugural lecture by Prof. Peter Scholze. (Video) In: YouTube.com. University of Bonn, June 9, 2017, accessed April 1, 2020 . 
16. ^ Hilmar Schmundt: Education. Better math than a rock band. In: Spiegel.de. April 23, 2016, accessed April 1, 2020 . 
17. ↑ Erica Klarreich: The Oracle of Arithmetic. In: QuantaMagazine.org. June 28, 2016, accessed April 1, 2020 . 
18. ↑ Bhargav Bhatt: What is… a Perfectoid Space? In: Notices of the AMS . tape 61 , no. 9 ( full text [PDF; 172 kB ; accessed on April 1, 2020]).
19. ↑ What are “perfectoid spaces”? Peter Scholze explains "Perfectoid Spaces". In: mathoverflow.net. 2011, accessed April 1, 2020 . 
20. ↑ Christoph Drösser: "Nobel Prize" for mathematics. The Bonn mathematician Peter Scholze receives the Fields Medal. In: Deutschlandfunk.de. August 1, 2018, accessed April 1, 2020 . 
21. ↑ Erica Klarreich: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture. In: QuantaMagazine.org. September 20, 2018, accessed April 1, 2020 . 
22. ↑ March 2018 Discussions on IUTeich. Mochizuki website with the report by Scholze and Stix and answers from Mochizuki. In: kurims.kyoto-u.ac.jp. Retrieved April 1, 2020 . 
23. ^ German professor chosen for SASTRA Ramanujan Prize. In: TheHindu.com . October 2, 2013, accessed April 1, 2020 . 
24. ^ Research Awards. In: Clay Mathematics Institute. Accessed April 28, 2020 (English). 
25. ↑ Peter Scholze to Receive 2015 AMS Cole Prize in Algebra. In: AMS.org. December 4, 2014, accessed April 1, 2020 . 
26. ↑ Breakthrough Prize Awarded $ 22 Million In Science Prizes. In: breakthroughprize.org. Retrieved April 1, 2020 . 
27. ↑ Prof. Dr. Peter Scholze - Gottfried Wilhelm Leibniz Prize Winner 2016. In: dfg.de. German Research Foundation, March 1, 2016, accessed April 1, 2020 . 
28. ↑ Member entry by Peter Scholze (with picture and curriculum vitae) at the German Academy of Natural Scientists Leopoldina , accessed on April 1, 2020.
29. ↑ Peter Scholze accepted into the academy as the youngest member. In: adwmainz.de. Academy of Sciences and Literature Mainz, January 16, 2017, accessed on April 1, 2020 . 
30. ^ Gisela Lerch: Berlin-Brandenburg Academy of Sciences elects four new members. Berlin-Brandenburg Academy of Sciences and Humanities, press release from June 9, 2017 at the Science Information Service (idw-online.de), accessed on April 1, 2020.
31. ↑ Peter Scholze is the new director at the Max Planck Institute for Mathematics. In: uni-bonn.de. July 12, 2018, accessed April 1, 2020 . 
32. ↑ Plenary Speakers. ( Memento of December 7, 2017 in the Internet Archive ). December 7, 2017. Retrieved December 14, 2017.
33. ↑ Laudation: For transforming arithmetic algebraic geometry over p-adic fields through his introduction of perfectoid spaces, with application to Galois representations, and for the development of new cohomology theories.
34. ^ Holger Dambeck: Fields Medal. Peter Scholze receives the highest award for mathematicians worldwide. In: Spiegel.de. August 1, 2018, accessed April 1, 2020 . 
35. ↑ Peter Scholze. Bonn mathematician receives Federal Cross of Merit. In: general-anzeiger-bonn.de. General Anzeiger Bonn, October 2, 2019, accessed on April 1, 2020 .