Caucher Birkar

Native spelling: کاوچر بیرکار

fl. 1978, Marivan, Kurdistan Province, Iran

AlgebraGeometryFields Medal 2018

Kurdish-British algebraic geometer at the University of Cambridge, specialist of birational geometry and the minimal model program; Fields Medalist 2018.

Caucher Birkar was born Fereydoun Derakhshani in 1978 in Marivan, a Kurdish city in western Iran near the Iraqi border, and grew up on a subsistence farm during the Iran–Iraq war. He studied mathematics at the University of Tehran, where he won a medal at the International Mathematics Competition for university students, before seeking asylum in the United Kingdom in 2000.

As a refugee he took the Kurdish name Caucher Birkar, meaning 'migrant mathematician'. He completed his PhD at the University of Nottingham in 2004, working on birational geometry in the tradition of Vyacheslav Shokurov's minimal model program. After positions at Cambridge and the National Center for Theoretical Sciences in Taiwan, he became professor at the University of Cambridge, and also holds a professorship at Tsinghua University in Beijing.

His landmark results include the 2010 paper with Cascini, Hacon and McKernan proving the existence of minimal models for varieties of general log type — which earned the quartet the 2016 AMS Moore Prize — and his 2016 proof of the boundedness of Fano varieties (the BAB conjecture). He received the Fields Medal in 2018; his medal was infamously stolen at the Rio de Janeiro ceremony and the IMU awarded him a replacement days later.

Workplaces: University of Cambridge, Tsinghua University

United Kingdom, Iran

Award-winning work

Fields Medal 2018Birkar was awarded the medal for the proof of the boundedness of Fano varieties and for contributions to the minimal model program. Fano varieties — the positively curved building blocks in the birational classification of algebraic varieties — were long expected but not known to form a bounded family in each dimension; Birkar proved this 'BAB' conjecture by controlling singularities of pairs and the behavior of anti-canonical divisors. Earlier, as part of the Birkar–Cascini–Hacon–McKernan collaboration, he had established the existence of minimal models and the finite generation of canonical rings for varieties of general type, completing a central part of the minimal model program envisioned by Mori.

Contributions, linked to the library

Library topicAlgebraic geometryProved the boundedness of Fano varieties and, with Cascini–Hacon–McKernan, the existence of minimal models — central advances in birational algebraic geometry.Library topicProjective geometryHis minimal model program results classify projective varieties up to birational equivalence by running controlled sequences of flips and contractions.