Caucher Birkar

Affiliation: YMSC , BIMSA

Email: caucherbirkar@bimsa.cn

Research Field: Algebraic Geometry

Webpage: https://ymsc.tsinghua.edu.cn/info/1031/2291.htm

Biography

Professor Birkar, the 2018 Fields Medalist, works in algebraic geometry, in particular, birational geometry. His work involves various topics such as minimal models,Fano and Calabi-Yau and general type varieties, singularity theory, positive characteristic geometry, etc.

Education Experience

2001 - 2004 The University of Nottingham Mathematics Doctor

Work Experience

2022 - BIMSA Professor
2006 - 2021 Cambridge University Professor
2004 - 2006 Warwick University Research Fellow

Honors and Awards

2019 Member of the Royal Society
2018 Fields Medal
2010 Prize of the Fondation Sciences Mathématiques de Paris
2010 Philip Leverhulme Prizes

Publication

[1] C. Birkar, Boundedness and volume of generalised pairs. arXiv:2103.14935v2.
[2] C. Birkar, Singularities of linear systems and boundedness of Fano varieties. Ann. of Math, 193, No. 2 (2021), 347–405.
[3] C. Birkar, G. Di Cerbo, R. Svaldi; Boundedness of elliptic Calabi-Yau varieties with a rational section. arXiv:2010.09769v1.
[4] C. Birkar, On connectedness of non-klt loci of singularities of pairs. arXiv:2010.08226v1.
[5] C. Birkar, Y. Chen, Singularities on toric fibrations. arXiv:2010.07651v1.
[6] C. Birkar, K. Loginov, Bounding non-rationality of divisors on 3-fold Fano fibrations. arXiv:2007.15754v1.
[7] C. Birkar, Generalised pairs in birational geometry. arXiv:2008.01008v2.
[8] C. Birkar, Geometry and moduli of polarised varieties.. arXiv:2006.11238v1 (2020).
[9] C. Birkar; Anti-pluricanonical systems on Fano varieties, Ann. of Math. 190, No. 2 (2019), 345–463.
[10] C. Birkar, Log Calabi-Yau fibrations. arXiv:1811.10709v2.
[11] C. Birkar, J. Waldron; Existence of Mori fibre spaces for 3-folds in char p. Adv. in Math. 313 (2017), 62-101.
[12] C. Birkar; The augmented base locus of real divisors over arbitrary fields. Math Ann. 368 (2017), no. 3-4, 905-921.
[13] C. Birkar, Y. Chen, L. Zhang, Iitaka’s Cn,m conjecture for 3-folds over finite fields. Nagoya Math. J., (2016), 1-31.
[14] C. Birkar, D.-Q. Zhang; Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs. Pub. Math. IHES 123 (2016), 283-331.
[15] C. Birkar; Existence of flips and minimal models for 3-folds in char p. Annales Scientifiques de l’ENS, 49 (2016), 169-212.
[16] C. Birkar; Singularities on the base of a Fano type fibration. J. Reine Angew Math., 715 (2016), 125-142.
[17] C. Birkar, Y. Chen; Images of manifolds with semi-ample anti-canonical divisor. J. Alg. Geom., 25 (2016), 273-287.
[18] C. Birkar, J.A. Chen; Varieties fibred over abelian varieties with fibres of log general type. Adv. in Math. 270 (2015), 206-222.
[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; On existence of log minimal models. Compos. Math. 146 (2010), 919-928.
[25] 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.
[26] C. Birkar; V.V. Shokurov; Mld’s vs thresholds and flips. J. Reine Angew. Math. 638 (2010), 209-234.
[27] C. Birkar; The Iitaka conjecture C n,m in dimension six. Compos. Math. 145 (2009), 1442-1446.
[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.

Update Time: 2025-06-04 14:44:06