Research:   Algebraic geometry (higher dimensional, birational, minimal model program). Papers: Boundedness and volume of generalised pairs, 2021 Boundedness of elliptic Calabi-Yau varieties with a rational section, 2020 On connectedness of non-klt loci of singularities of pairs, 2020 Singularities on toric fibrations, 2020 Bounding non-rationality of divisors on 3-fold Fano fibrations , 2020 Geometry and moduli of polarised varieties, 2020 Generalised pairs in birational geometry, 2020 Log Calabi-Yau fibrations, 2018 Singularities of linear systems and boundedness of Fano varieties, Ann. of Math, 193, No. 2 (2021), 347–405. Anti-pluricanonical systems on Fano varieties, Ann. of Math. Vol. 190, No. 2 (2019), pp. 345–463. Iitaka's Cn,m conjecture for 3-folds over finite fields, Nagoya Math. J., (2016), 1–31 (Joint with Yifei Chen and Lei Zhang) Existence of Mori fibre spaces for 3-folds in char p, Adv. in Math 313 (2017) 62–101 (Joint with Joe Waldron) Effetivity of Iitaka fibrations and pluricanonical systems of polarized pairs, Pub. Math. IHES., 123 (2016), 283–331. (Joint with De-Qi Zhang) The augmented base locus of real divisors over arbitrary fields, Math. Ann. (2017) 368:905–921. Varieties fibred over abelian varieties with fibres of log general type, Advances in Math. Volume 270 (2015), 206–222. (joint with Jungkai Chen) Erratum Existence of flips and minimal models for 3-folds in char p, Annales scientifiques de l'ENS 49, 1 (2016), 169-212. Log canonical pairs with good augmented base loci, Compositio Math. Volume 150 (2014), 579-592. (joint with Zhengyu Hu) Polarized pairs, log minimal models, and Zariski decompositions (original title was: On log minimal models and Zariski decompositions II), Nagoya Math. J. Volume 215 (2014), 203-224. (joint with Zhengyu Hu) Singularities on the base of a Fano type fibration, J. Reine Angew Math. (2016), Issue 715. Images of manifolds with semi-ample anti-canonical divisor (this appeared on arxiv as "On the moduli part of the Kawamata-Kodaira canonical bundle formula"). J. Algebraic Geom. 25 (2016), 273-287. (joint with Yifei Chen) Divisorial algebras and modules on schemes, 2011. A short version appeared in J. Math. Soc. Japan Volume 65, Number 4 (2013), 1319-1328. Existence of log canonical flips and a special LMMP. Pub. Math. IHES. Volume 115 (2012), Issue 1, 325-368. Supplement to the paper "On existence of log minimal models II", 2011. This paper appears as a section of the previous paper. On existence of log minimal models and weak Zariski decompositions, Math Annalen, Volume 354 (2012), Number 2, 787-799. On existence of log minimal models II, J. Reine Angew Math. 658 (2011), 99-113. Minimal models, flips and finite generation : a tribute to V.V. SHOKUROV and Y.-T. SIU, In "Classification of algebraic varieties", European Math Society series of congress reports (2010) (joint with Mihai Paun) Iitaka conjecture C_{n,m} in dimension six. Compositio Math. volume 145 (2009), 1442-1446. On termination of log flips in dimension four. Math. Ann. volume 346, no 2 (2009), 251-257. Log minimal models according to Shokurov. J. Algebra and Number Theory, volume 3, no 8 (2009), 951-958. On existence of log minimal models. Compositio Mathematica 146 (2010), 919-928. Existence of minimal models for varieties of log general type.   (joint with Cascini, Hacon and McKernan) J. Amer. Math. Soc. 23 (2010), 405-468. Mld's vs thresholds and flips. (joint with Shokurov). J. Reine Angew Math, 638 (2010), 209-234. Ascending chain condition for log canonical thresholds and termination of log flips. Duke Math. J. Volume 136, Number 1 (2007), 173-180. PhD thesis, 2004 Boundedness of epsilon-lc complements on surfaces II, 2004 Boundedness of epsilon-lc complements on surfaces, 2004 On Shokurov's log flips: the 3-dimensional case, 2002 Elements of nonstandard algebraic geometry, 2001 Talks: Minimal model program and moduli spaces, 2007 (Hokkaido University, Japan) A complete list of talks (up to October 2011)