Caucher Birkar

Caucher Birkar (2018)

Caucher Birkar ( Kurdish کۆچەر بیرکار Koçer Bîrkar , German “Migrated Mathematician” ; * July 1978 in Marivan , Kordestān , Iran asفریدون درخشانی Fereydon Derakhshani ) is a British-Iranianmathematician of Kurdishorigin who studiesalgebraic geometry. He is a professor atCambridge Universityand recipient of theFields Medal.

Life

Birkar grew up in the countryside in the Kurdish part of western Iran. His parents were farmers. He studied at the University of Tehran , applied for asylum on a visit to England and studied at the University of Nottingham from 2001 , where he received his doctorate in 2004 under Ivan Fesenko (Topics in modern algebraic geometry). During this time, Birkar was also a student of Vyacheslav Vladimirovich Shokurov , who revived the minimal model program in the early 2000s (among other things, he proved the existence of flips in four dimensions).

He is married and has a son.

plant

Birkar is concerned with the program of minimal models in higher-dimensional ( birational ) algebraic geometry by Shigefumi Mori (1990 Fields Medal Winner and Chairman of the Fields Prize Committee 2018). Mori was able to show the birational classification of algebraic varieties in three dimensions. There are essentially three types: Fano varieties (Fano-Mori fiber spaces, positive curvature ), Calabi-Yau varieties (Calabi-Yau fiber spaces, flat) and varieties of the general type (with negative curvature). Research in this area was at a standstill for a long time, but experienced a renewed boom in the 2000s. With Christopher Hacon , James McKernan and Paolo Cascini , Birkar made advances in the classification of general type varieties in 2006 (they showed the existence of flips in more than two dimensions and the existence of minimal models for general type varieties). In 2016 he was able to show that Fano varieties in any dimension (and with mild singularities ) can be characterized by a finite number of parameters. With this, he proved a presumption by Borisov-Alexeev-Borisov. He also made significant advances in the treatment of various types of singularities that play a role in the Minimal Model Program . He also dealt with the Minimal Model Program for varieties over bodies with positive characteristics and, building on the work of Hacon and Chenyang Xu , proved the existence of log flips and log minimal models in three dimensions for . ${\displaystyle p}$ ${\displaystyle p>5}$

Fields Medal

On August 1, 2018, Birkar won the Fields Medal together with Alessio Figalli , Peter Scholze and Akshay Venkatesh . It is also considered the Nobel Prize in Mathematics and is awarded every four years to up to four mathematicians under the age of 40. It was stolen from him just an hour after Birkar received it. The International Congress of Mathematicians , which organized the award ceremony, then announced that Birkar would receive a new Fields Medal.

Awards

• 2010 Prix de la Fondation Sciences mathematiques de Paris
• 2010 Leverhulme Prize
• 2016 AMS EH Moore Research Article Prize of the American Mathematical Society with Hacon, McKernan and Cascini for their essay Existence of minimal models for varieties of log general typ.
• 2018 Whitehead Prize
• 2018 Fields Medal “for demonstrating the limitedness of Fano varieties and contributions to the program of minimal models” (laudatory speech).
• 2019 member of the Royal Society

Fonts (selection)

• Birational Geometry. 2007.
• Topics in Algebraic Geometry. Lecture 2011.
• With Hacon, Cascini, McKernan: Existence of minimal models for varieties of log general type I. Journal of the American Mathematical Society, Volume 23, 2010, pp. 405-468.
• Anti-pluricanonical systems on Fano varieties. 2016.
• Singularities of linear systems and boundedness of Fano varieties. 2016.
• Birational geometry of algebraic varieties. ICM 2018.

Web links

• Homepage
• Videos from and about Caucher Birkar in the AV portal of the Technical Information Library

Individual evidence

1. ↑ ^{a b} Kevin Hartnett: An Innovator Who Brings Order to an Infinitude of Equations. In: QuantaMagazine.org. August 1, 2018, accessed August 3, 2018 . 
2. ↑ Caucher Birkar in the Mathematics Genealogy Project (English)
3. ↑ Fields Medal stolen shortly after it was awarded in Brazil. In: nzz.ch. Neue Zürcher Zeitung, August 2, 2018, accessed on August 3, 2018 . 
4. ↑ Top math laureate gets new medal after prize stolen. In: AFP.com. August 3, 2018, archived from the original on August 3, 2018 ; accessed on August 3, 2018 . 
5. ↑ Le cours de Caucher Birkar. In: sciencesmaths-paris.fr. Retrieved August 3, 2018 (French). 
6. ↑ Caucher Birkar has been awarded 2010 Philip Leverhulme prize. In: wordpress.com. Geometry Bulletin Board, November 22, 2010, accessed August 3, 2018 . 
7. ↑ Cambridge mathematician awarded 2018 Fields Medal. In: cam.ac.uk. University of Cambridge, August 1, 2018, accessed August 3, 2018 . 
8. ↑ 2018 LMS Prize Winners. In: lms.ac.uk. London Mathematical Society, accessed August 3, 2018 . 
9. ↑ Fields Medals 2018. Caucher Birkar. In: mathunion.org. Retrieved September 15, 2018 : "For the proof of the boundedness of Fano varieties and for contributions to the minimal model program."