Caucher Birkar
Caucher Birkar | |
|---|---|
| Born | 1978 (age 45–46) Marivan, Iran |
| Citizenship | British and Iranian |
| Alma mater | University of Tehran University of Nottingham |
| Known for | flips, minimal models, finite generation, pluricanonical systems, boundedness of Fano varieties, char p geometry |
| Awards | Leverhulme Prize 2010 Prize of the Fondation Sciences Mathématiques de Paris 2010 AMS Moore Prize 2016 Fields Medal 2018 |
| Scientific career | |
| Fields | Higher-dimensional and birational algebraic geometry |
| Institutions | University of Cambridge |
| Doctoral advisor | Ivan Fesenko and Vyacheslav Shokurov |
| Website | https://www.dpmms.cam.ac.uk/~cb496/ |
Caucher Birkar (born July 1978, Kurdish: کۆچەر بیرکار), also known as Fereydoun Derakhshani (فریدون درخشانی), is an Iranian Kurdish mathematician and a British citizen. He is a professor at the University of Cambridge. Birkar is a main contributor to modern birational geometry. In 2010 he received the Leverhulme Prize in mathematics and statistics for his contributions to algebraic geometry.[1] and, in 2016, the AMS Moore Prize[2] for the article "Existence of minimal models for varieties of log general type," Journal of the AMS (2010) (joint with P. Cascini, C. Hacon and J. McKernan). He was awarded the Fields Medal in 2018, "for his proof of boundedness of Fano varieties and contributions to minimal model problem".
Early years and education
Birkar was born in 1978 in Marivan, Kurdistan Province, Iran, where he spent his school years. He studied mathematics at the University of Tehran where he received his bachelor's degree. He was awarded the third prize in the International Mathematics Competition for University Students in 2000 [3] and, shortly after, relocated to the UK as a refugee[4], in 2001–2004 Birkar was a PhD student at the University of Nottingham. In 2003 he was awarded the London Mathematical Society Prize as the most promising PhD student.[citation needed]
Research
Birkar's main area of interest is algebraic geometry, in particular, higher dimensional birational geometry. He studied fundamental aspects of key problems in modern mathematics such as minimal models, Fano varieties, singularities, and linear systems. His theories provided solutions of various long-standing conjectures.[citation needed]
Together with Paolo Cascini, Christopher Hacon and James McKernan he settled several important conjectures including existence of log flips, finite generation of log canonical rings, and existence of minimal models for varieties of log general type, building upon earlier work of Vyacheslav Shokurov and of Hacon and McKernan.[5] He also showed that the minimal model conjecture follows from the abundance conjecture and established links between the former conjecture and various other notions such as log canonical thresholds and Zariski decompositions.
In the setting of log canonical singularities, he proved existence of log flips along with key cases of the minimal model and abundance conjectures. (This was also proved independently by Hacon and Chenyang Xu.)[6]
In a different direction, he studied the old problem of Iitaka on effectivity of Iitaka fibrations induced by pluri-canonical systems on varieties of non-negative Kodaira dimension. The problem consists of two halves: one related to general fibres of the fibration and one related to the base of the fibration. Birkar and co solved the second half of the problem, hence essentially reducing Iitaka's problem to the special case of Kodaira dimension zero.[7]
In more recent work, Birkar studied Fano varieties and singularities of linear systems. He proved several fundamental problems such as Shokurov's conjecture on boundedness of complements and Borisov-Alexeev-Borisov conjecture on boundedness of Fano varieties.[8][9] This direction is viewed to have fundamental applications in birational geometry. Birkar answered a question of Gang Tian on alpha-invariants and answered a question of Jean-Pierre Serre on Jordan property of Cremona groups building on the work of Yuri Prokhorov and Constantin Shramov.[citation needed]
Birkar is also active in the field of birational geometry over fields of positive characteristic. His work together with work of Hacon-Xu nearly completes the minimal model program for 3-folds over fields of characteristic at least 7.[10]
Awards
- 2010 Leverhulme Prize in mathematics and statistics for "his outstanding contributions to fundamental research in algebraic geometry"[1][11]
- 2010 Prize of the Fondation Sciences Mathématiques de Paris[12]
- 2016 AMS Moore Prize [13]
- 2018 Fields Medal. Birkar's Fields Medal was stolen from him on the same day it was awarded to him.[14]
References
- ^ a b "Archived copy". Archived from the original on 2013-06-10. Retrieved 2012-12-30.
{{cite web}}: Unknown parameter|deadurl=ignored (|url-status=suggested) (help)CS1 maint: archived copy as title (link) - ^ "American Mathematical Society". www.ams.org. Retrieved 1 August 2018.
- ^ http://www.ucl.ac.uk/~ucahjej/imc/imc2000/results.html
- ^ Fields medal: UK refugee wins 'biggest maths prize', by Paul Rincon, at BBC.co.uk; published August 1, 2018; retrieved August 1, 2018
- ^ C. Birkar, P. Cascini, C. Hacon, J. McKernan Existence of minimal models for varieties of log general type, J. Amer. Math. Soc. 23 (2010), 405–468.
- ^ C. Birkar, Existence of log canonical flips and a special LMMP, Pub. Math. IHES 115 (2012), Issue 1, 325–368.
- ^ C. Birkar, D.-Q. Zhang, Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs. To appear in Pub. Math IHES.
- ^ C. Birkar, Anti-pluricanonical systems on Fano varieties. arXiv:1603.05765
- ^ C. Birkar, Singularities of linear systems and boundedness of Fano varieties. arXiv:1609.05543.
- ^ C. Birkar, Existence of flips and minimal models for 3-folds in char p. Annales scientifiques de l’ENS 49 (2016), 169-212.
- ^ "Caucher Birkar has been awarded 2010 Philip Leverhulme prize". wordpress.com. 22 November 2010. Retrieved 1 August 2018.
- ^ http://www.sciencesmaths-paris.fr/en/Researchers%20and%20Students-285.htm
- ^ http://www.ams.org/news?news_id=2873
- ^ Phillips, Dom (1 August 2018). "World's most prestigious maths medal is stolen minutes after professor wins it". The Guardian.
External links
- [1], some of his papers
- Caucher Birkar at the Mathematics Genealogy Project
- Birkar on Journalogy
- Caucher Birkar publications indexed by the Scopus bibliographic database. (subscription required)
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