Caucher Birkar
Professor
Affiliation: YMSC, BIMSA
Group: Algebraic Geometry
Email: birkar@mail.tsinghua.edu.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 (2020)
- [4] C. Birkar, On connectedness of non-klt loci of singularities of pairs (2020)
- [5] C. Birkar, Y. Chen, Singularities on toric fibrations (2020)
- [6] C. Birkar, K. Loginov, Bounding non-rationality of divisors on 3-fold Fano fibrations (2020)
- [7] C. Birkar, Generalised pairs in birational geometry. (2020)
- [8] C. Birkar, Geometry and moduli of polarised varieties (2020)
- [9] C. Birkar, Anti-pluricanonical systems on Fano varieties, Ann. of Math., 190(2), 345–463 (2019)
- [10] C. Birkar, Log Calabi-Yau fibrations., arXiv:1811.10709v2. (2018)
- [11] C. Birkar, J. Waldron, Existence of Mori fibre spaces for 3-folds in char p., Adv. in Math., 313(2017), 62-101 (2017)
- [12] C. Birkar, The augmented base locus of real divisors over arbitrary fields., Math Ann.(3-4), 905-921 (2017)
- [13] C. Birkar, Y. Chen, L. Zhang, Iitaka’s Cn,m conjecture for 3-folds over finite fields., Nagoya Math. J., 1-31 (2016)
- [14] C. Birkar, D.-Q. Zhang, Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs., Pub. Math. IHES, 123, 283-331 (2016)
- [15] C. Birkar, Existence of flips and minimal models for 3-folds in char p., Annales Scientifiques de l’ENS, 49(2016), 169-212 (2016)
- [16] C. Birkar, Singularities on the base of a Fano type fibration., J. Reine Angew Math., 715(125-142) (2016)
- [17] C. Birkar, Y. Chen, Images of manifolds with semi-ample anti-canonical divisor., J. Alg. Geom., 25(1), 273-287 (2016)
- [18] C. Birkar, J.A. Chen, Varieties fibred over abelian varieties with fibres of log general type., Adv. in Math., 270(2015), 206-222 (2015)
- [19] C. Birkar, Z. Hu, Log canonical pairs with good augmented base loci., Compos. Math, 150(4), 579-592 (2014)
- [20] C. Birkar, Z. Hu, Polarized pairs, log minimal models, and Zariski decompositions, Nagoya Math. J., 215(2014), 203-224 (2014)
- [21] C. Birkar, Existence of log canonical flips and a special LMMP., Pub. Math. IHES, 115(1), 325-368 (2012)
- [22] C. Birkar, On existence of log minimal models and weak Zariski decompositions, Math Ann., 354(2), 787-799 (2012)
- [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] Caucher Birkar, Paolo Cascini, Christopher D. Hacon and James McKernan, Existence of minimal models for varieties of log general type, J. Amer. Math. Soc., 23, 405-468 (2010)
- [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., 1442-1446. (2009)
- [28] C. Birkar, Ascending chain condition for log canonical thresholds and termination of log flips., Duke Math. Journal, 136(1), 173-180 (2007)
Update Time: 2025-07-23 17:52:45