Research Areas

algebraic geometry, particularly birational geometry, an area with deep connections with many other parts of mathematics such as differential geometry, arithmetic geometry, group theory, mirror symmetry, mathematical physics, etc 

Educational Background

2001-2004  Doctor, University of Nottingham

Work Experience

Present: University of Cambridge

Honors and Awards

Fellow of the Royal Society, 2019.
Fields Medal, 2018.
Philip Leverhulme prize, 2010.
Prize of the Fondation Sciences Mathématiques de Paris, 2010.


(1) C. Birkar, Boundedness and volume of generalised pairs. arXiv:2103.14935v2.
(2) C. Birkar, G. Di Cerbo, R. Svaldi; Boundedness of elliptic Calabi-Yau varieties with a rational section.
(3) C. Birkar, On connectedness of non-klt loci of singularities of pairs. arXiv:2010.08226v1.
(4) C. Birkar, Y. Chen, Singularities on toric fibrations. arXiv:2010.07651v1.
(5) C. Birkar, K. Loginov, Bounding non-rationality of divisors on 3-fold Fano fibrations. arXiv:2007.15754v1.
(6) C. Birkar, Generalised pairs in birational geometry. arXiv:2008.01008v2.
(7) C. Birkar, Geometry and moduli of polarised varieties.. arXiv:2006.11238v1 (2020).
(8) C. Birkar, Log Calabi-Yau fibrations. arXiv:1811.10709v2.
(9) C. Birkar, Singularities of linear systems and boundedness of Fano varieties. Ann. of Math, 193, No. 2
(2021), 347–405.
(10) C. Birkar; Anti-pluricanonical systems on Fano varieties, Ann. of Math. 190, No. 2 (2019), 345–463.
(11) C. Birkar, Y. Chen, L. Zhang, Iitaka’s Cn,m conjecture for 3-folds over finite fields. Nagoya Math. J., (2016), 1-31.
(12) C. Birkar, J. Waldron; Existence of Mori fibre spaces for 3-folds in char p. Adv. in Math. 313 (2017), 62-101.
(13) C. Birkar, D.-Q. Zhang; Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs. Pub. Math. IHES
123 (2016), 283-331.
(14) C. Birkar; The augmented base locus of real divisors over arbitrary fields. Math Ann. 368 (2017), no. 3-4, 905-921.
(15) C. Birkar, J.A. Chen; Varieties fibred over abelian varieties with fibres of log general type. Adv. in Math. 270 (2015),
(16) C. Birkar; Existence of flips and minimal models for 3-folds in char p. Annales Scientifiques de l’ENS,
49 (2016), 169-212.
(17) C. Birkar; Singularities on the base of a Fano type fibration. J. Reine Angew Math., 715 (2016), 125-142.
(18) C. Birkar, Y. Chen; Images of manifolds with semi-ample anti-canonical divisor. J. Alg. Geom., 25 (2016), 273-287.
(19) C. Birkar, Z. Hu; Log canonical pairs with good augmented base loci. Compos. Math, 150, 04, (2014), 579-592.
(20) C. Birkar, Z. Hu; Polarized pairs, log minimal models, and Zariski decompositions. Nagoya Math. J.
Volume 215 (2014), 203-224.
(21) C. Birkar; Existence of log canonical flips and a special LMMP. Pub. Math. IHES. Volume 115 (2012), 1, 325-368.
(22) C. Birkar; On existence of log minimal models and weak Zariski decompositions. Math Ann., Volume
354 (2012), Number 2, 787-799.
(23) C. Birkar; On existence of log minimal models II. J. Reine Angew Math. 658 (2011), 99-113.
(24) C. Birkar; The Iitaka conjecture C n,m in dimension six. Compos. Math. 145 (2009), 1442-1446.
(25) C. Birkar; On existence of log minimal models. Compos. Math. 146 (2010), 919-928.
(26) C. Birkar; P. Cascini; C. Hacon; J. M c Kernan; Existence of minimal models for varieties of log general
type. J. Amer. Math. Soc. 23 (2010), 405-468.
(27) C. Birkar; V.V. Shokurov; Mld’s vs thresholds and flips. J. Reine Angew. Math. 638 (2010), 209-234.
(28) C. Birkar; Ascending chain condition for log canonical thresholds and termination of log flips. Duke
Math. Journal, volume 136, no 1, (2007), 173-180.×××