Caucher Birkar ( ku, کۆچەر بیرکار, lit=migrant mathematician, translit=Koçer Bîrkar; born Fereydoun Derakhshani ( fa, فریدون درخشانی); July 1978) is an

Iranian Iranian may refer to: * Iran, a sovereign state * Iranian peoples, the speakers of the Iranian languages. The term Iranic peoples is also used for this term to distinguish the pan ethnic term from Iranian, used for the people of Iran * Iranian lan ...

Kurdish Kurdish may refer to: *Kurds or Kurdish people *Kurdish languages *Kurdish alphabets *Kurdistan, the land of the Kurdish people which includes: **Southern Kurdistan **Eastern Kurdistan **Northern Kurdistan **Western Kurdistan See also * Kurd (dis ...

mathematician and a professor at

Tsinghua University Tsinghua University (; abbreviation, abbr. THU) is a National university, national Public university, public research university in Beijing, China. The university is funded by the Ministry of Education of the People's Republic of China, Minis ...

and

University of Cambridge , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...

. Birkar is an important contributor to modern

birational geometry In mathematics, birational geometry is a field of algebraic geometry in which the goal is to determine when two algebraic varieties are isomorphic outside lower-dimensional subsets. This amounts to studying mappings that are given by rational fu ...

. In 2010 he received the

Leverhulme Prize The Philip Leverhulme Prize is awarded by the Leverhulme Trust to recognise the achievement of outstanding researchers whose work has already attracted international recognition and whose future career is exceptionally promising. The prize schem ...

in mathematics and statistics for his contributions to

algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

, and in 2016, shared the AMS Moore Prize for the article "Existence of minimal models for varieties of log general type". He was awarded the

Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award ho ...

in 2018, "for his proof of boundedness of

Fano varieties In algebraic geometry, a Fano variety, introduced by Gino Fano in , is a complete variety ''X'' whose anticanonical bundle ''K''X* is ample. In this definition, one could assume that ''X'' is smooth over a field, but the minimal model program has ...

and contributions to the

minimal model program In algebraic geometry, the minimal model program is part of the birational classification of algebraic varieties. Its goal is to construct a birational model of any complex projective variety which is as simple as possible. The subject has its orig ...

". In his office at the University, Birkar has two photographs of Alexander Grothendieck, his favorite mathematician, who like Birkar, was a refugee and Fields medalist.

Early life and education

Birkar is a

Kurd ug:كۇردلار Kurds ( ku, کورد ,Kurd, italic=yes, rtl=yes) or Kurdish people are an Iranian peoples, Iranian ethnic group native to the mountainous region of Kurdistan in Western Asia, which spans southeastern Turkey, northwestern Ir ...

, born in 1978 in

Marivan County Marivan County ( fa, شهرستان مریوان, ku, شارستانی مەریوان) is in Kurdistan province, Iran. The capital of the county is the city of Marivan. Marivan County is bordered by Saqqez County to the north, Sanandaj Cou ...

, Kurdistan province,

Iran Iran, officially the Islamic Republic of Iran, and also called Persia, is a country located in Western Asia. It is bordered by Iraq and Turkey to the west, by Azerbaijan and Armenia to the northwest, by the Caspian Sea and Turkmeni ...

, on a subsistence farm, and raised during the Iran-Iraq War. He had five siblings, and learned a lot of mathematics from his brothers during the first years of school. Following his graduation from high school, Birkar studied mathematics at the

University of Tehran The University of Tehran (Tehran University or UT, fa, دانشگاه تهران) is the most prominent university located in Tehran, Iran. Based on its historical, socio-cultural, and political pedigree, as well as its research and teaching pro ...

where he received his bachelor's degree. He was awarded the third prize in the

International Mathematics Competition for University Students The International Mathematics Competition (IMC) for University Students is an annual mathematics competition open to all undergraduate students of mathematics. Participating students are expected to be at most twenty three years of age at the time ...

in 2000 and, shortly after, while still studying in the University, relocated to the UK as a

refugee A refugee, conventionally speaking, is a displaced person who has crossed national borders and who cannot or is unwilling to return home due to well-founded fear of persecution.

and asked for

political asylum The right of asylum (sometimes called right of political asylum; ) is an ancient juridical concept, under which people persecuted by their own rulers might be protected by another sovereign authority, like a second country or another enti ...

.Fields medal: UK refugee wins 'biggest maths prize'
by Paul Rincon, at

BBC.co.uk BBC Online, formerly known as BBCi, is the BBC's online service. It is a large network of websites including such high-profile sites as BBC News and BBC Sport, Sport, the on-demand video and radio services branded BBC iPlayer and BBC Sounds, t ...

; published 1 August 2018; retrieved 1 August 2018 In 2001–2004 Birkar was a PhD student at the

University of Nottingham The University of Nottingham is a public university, public research university in Nottingham, United Kingdom. It was founded as University College Nottingham in 1881, and was granted a royal charter in 1948. The University of Nottingham belongs t ...

. In 2003 he was awarded the Cecil King Travel Scholarship by the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...

as the most promising PhD student. Upon emigrating to the UK he changed his name to Caucher Birkar, which means "migrant mathematician" in

Research and career

Together with Paolo Cascini,

Christopher Hacon Christopher Derek Hacon (born 14 February 1970) is a mathematician with British, Italian and US nationalities. He is currently distinguished professor of mathematics at the University of Utah where he holds a Presidential Endowed Chair. His res ...

and

James McKernan James McKernan (born 1964) is a mathematician, and a professor of mathematics at the University of California, San Diego. He was a professor at MIT from 2007 until 2013. Education McKernan was educated at the Campion School, Hornchurch, and Tr ...

, Birkar settled several conjectures including existence of log

flips Flip, FLIP, or flips may refer to: People * Flip (nickname), a list of people * Lil' Flip (born 1981), American rapper * Flip Simmons, Australian actor and musician * Flip Wilson, American comedian Arts and entertainment Fictional characters * ...

, finite generation of log

canonical ring In mathematics, the pluricanonical ring of an algebraic variety ''V'' (which is non-singular), or of a complex manifold, is the graded ring :R(V,K)=R(V,K_V) \, of sections of powers of the canonical bundle ''K''. Its ''n''th graded component (for ...

s, and existence of minimal models for varieties of log general type, building upon earlier work of

Vyacheslav Shokurov Vyacheslav Vladimirovich Shokurov (russian: Вячеслав Владимирович Шокуров; born 18 May 1950) is a Russian mathematician best known for his research in algebraic geometry. The proof of the Noether–Enriques–Petri the ...

and of Hacon and McKernan. In the setting of log canonical singularities, he proved existence of log flips along with key cases of the minimal model and

abundance conjecture In algebraic geometry, the abundance conjecture is a conjecture in birational geometry, more precisely in the minimal model program, stating that for every projective variety X with Kawamata log terminal singularities over a field k if the canonic ...

s. (This was also proved independently by Hacon and

Chenyang Xu Chenyang Xu (; born 1981) is a Chinese mathematician in the area of algebraic geometry and a professor at Princeton University. Xu is known for his work in birational geometry, the minimal model program, and the K-stability of Fano varieties. ...

.) 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 In algebraic geometry, the Kodaira dimension ''κ''(''X'') measures the size of the canonical ring, canonical model of a projective variety ''X''. Igor Shafarevich, in a seminar introduced an important numerical invariant of surfaces with the ...

. 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 Zhang co-solved the second half of the problem, hence essentially reducing Iitaka's problem to the special case of Kodaira dimension zero. In more recent work, Birkar studied Fano varieties and singularities of linear systems. He has solved several fundamental problems such as Shokurov's conjecture on boundedness of complements, and the Borisov–Alexeev–Borisov conjecture on boundedness of Fano varieties. In 2018, Birkar was given the

for his work on

and other contributions to the minimal model problem. In a video made available by the

Simons Foundation The Simons Foundation is a private foundation established in 1994 by Marilyn and Jim Simons with offices in New York City. As one of the largest charitable organizations in the US with assets of over $5 billion in 2022, the foundation's mission ...

, Birkar expressed hope that his Fields Medal will put "just a little smile on the lips" of the world's estimated 40 million Kurds. Birkar's Fields Medal was stolen on the same day it was awarded to him. In a special ceremony at ICM 2018, Birkar was presented with a replacement medal, leading to quips he was the first person to receive the Fields Medal ''twice''. 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.

Awards and honours

* 2010

in mathematics and statistics for "his outstanding contributions to fundamental research in algebraic geometry" * 2010 Prize of the Fondation Sciences Mathématiques de Paris * 2016 AMS Moore Prize * 2018

* 2019 Honorary Doctorate of the Salahaddin University, Erbil

Early life and education

Research and career

Awards and honours

References

Further reading