Professional Profile: ArXiv, Mathscinet, zbMATH, Google Scholar,
Research
2009-2012
1. Congruence for rational points over finite fields and coniveau over local fields (with H. Esnault). Trans. Amer. Math. Soc. 361 (2009), no. 5, 2679-2688.
2. Degenerations of Rationally Connected Varieties (with A. Hogadi). Trans. Amer. Math. Soc. 361 (2009), No.7, 3931-3949.
3. Notes on π1 of Smooth Loci of Log Del Pezzo Surfaces. Michigan Math. J. 58 (2009), no. 2. 489-515.
4. On Effective Log Iitaka Fibration for 3-folds and 4-folds (with G. Todorov). Algebra Number Theory 3 (2009), no. 6, 697-710.
5. Log-canonical models of singular pairs and its applications (with Yuji Odaka). Math. Res. Lett. 19 (2012), no.2, 325-334.
6. Strong rational connectedness of surfaces. J. Reine Angew. Math. 665 (2012), 189-205.
7. Weak approximation for low degree del Pezzo surfaces. Journal of Algebraic Geometry 21 (2012), 753-767.
2013-2014
8. On the birational automorphisms of varieties of general type (with Christopher Hacon and James McKernan). Annals of Math. 177 (2013), Issue 3, 1077-1111.
9. Existence of log canonical closures (with Christopher Hacon). Invent. Math. 192 (2013), Issue 1, 161-195.
10. Finiteness of algebraic fundamental groups. Compos. Math. 150 (2014), Issue 03, 409-414.
11. Special test configurations and K-stability of Fano varieties (with Chi Li). Annals of Math. 180 (2014), Issue 1, 197-232.
12. ACC for log canonical thresholds (with Christopher Hacon and James McKernan). Annals of Math. 180 (2014), Issue 2, 523-571.
13. Nonexistence of aymptotic GIT compactification (with Xiaowei Wang). Duke Math. J. 163 (2014), Issue 12, 2217-2241.
2015
14. On the three dimensional minimal model program in positive characteristic (with Christopher Hacon). J. Amer. Math. Soc. 28 (2015) no. 3, 711-744.
15. On base point free theorem of threefolds in positive characteristic. J. Inst. Math. Jussieu 14 (2015) Issue 3, 577-588.
16. On base point freeness in positive characteristic (with Paolo Cascini and Hiromu Tanaka). Ann. Sci. École Norm. Sup. 48 (2015) no. 5, 1239-1272.
17. Boundedness of log Calabi-Yau pairs of Fano type (with Christopher Hacon). Math. Res. Lett. 22 (2015), no.6, 1699-1716.
2016-2018
18. Poles of maximal order of motivic zeta function (with Johannes Nicaise). Duke Math. J. 165 (2016), Issue 2, 217-243.
19. Motivic zeta function via dlt modification. Michigan Math. J. 65 (2016), Issue 1, 89-103.
20. The dual complex of Calabi-Yau pairs (with János Kollár). Invent. Math. 205 (2016), Issue 3, 527-557.
21. On Finiteness of B-representations and Semi-log Canonical Abundance (with Christopher Hacon). Minimal models and extremal Rays (Kyoto, 2011), 361-378, Adv. Stud. in Pure Math 70, Math. Soc. Japan, Tokyo, 2016.
22. The essential skeleton of a degeneration of algebraic varieties (with Johannes Nicaise). Amer. J. Math. 138 (2016), No. 6, 1645-1667.
23. Ampleness of the CM line bundle on the moduli space of canonically polarized varieties (with Zsolt Patakfalvi). Algebraic Geometry 4 (2017) Issue 1, 29-39.
24. Finiteness of fundamental groups (with Zhiyu Tian). Compos. Math. 153 (2017), Issue 02, 257-273.
25. The dual complex of singularities (with Tommaso de Fernex, János Kollár). Higher Dimensional Algebraic Geometry in honour of Professor Yujiro Kawamata’s sixtieth birthday, 103-129, Adv. Stud. in Pure Math 74, Math. Soc. Japan, Tokyo, 2017.
26. Semi-stable extensions over 1-dimensional bases (with János Kollár and Johannes Nicaise). Acta Math. Sinica 34 (2018), Issue 1, 103-113.
27. Boundedness of moduli of varieties of general type (with Christopher Hacon and James McKernan). J. Euro. Math. Soc. 20 (2018), Issue 4, 865-901.
28. Quasi-projectivity of the moduli space of smooth Kähler-Einstein Fano manifolds (with Chi Li and Xiaowei Wang). Ann. Sci. École Norm. Sup. 51 (2018) no. 3, 739-772.
29. Stability of Valuations: Higher Rational Rank (with Chi Li). Peking Math. J. 1 (2018) no. 1, 1-79.
2019-2022
30. The non-archimedean SYZ fibration (with Johannes Nicaise, Tony Yue Yu). Compos. Math. 155 (2019), Issue 05, 953-972.
31. Nonvanishing for threefolds in characteristic p > 5 (with Lei Zhang). Duke Math. J. 168 (2019), Issue 07, 1269-1301.
32. On the proper moduli spaces of smoothable Kähler-Einstein Fano varieties (with Chi Li and Xiaowei Wang). Duke Math. J. 168 (2019), Issue 08, 1387-1459.
33. K-stability of cubic threefolds (with Yuchen Liu). Duke Math. J. 168 (2019), Issue 11, 2029-2073.
34. Uniqueness of K-polystable degenerations of Fano varieties (with Harold Blum). Annals of Math. 190 (2019), Issue 2, 609-656.
35. A minimizing valuation is quasi-monomial. Annals of Math. 191 (2020), Issue 3, 1003-1030.
36. Moduli of polarized Calabi-Yau pairs (with János Kollár). Acta Math. Sinica 36 (2020), Issue 6, 631-637.
37. Stability of Valuations and Kollár Components (with Chi Li). J. Euro. Math. Soc. 22 (2020), Issue 8, 2573-2627.
38. Reductivity of the automorphism group of K-polystable Fano varieties (with Jarod Alper, Harold Blum and Daniel Halpern-Leistner). Invent. Math. 222 (2020), Issue 3, 995-1032.
39. On positivity of the CM line bundle on K-moduli spaces (with Ziquan Zhuang). Annals of Math. 192 (2020), Issue 3, 1005-1068.
40. Rational points of rationally simply connected varieties over global functional fields (with Jason Starr). Ann. H. Lebesgue 3 (2020), 1399-1417.
41. Towards finite generation of higher rational rank valuations. Sb. Math. 212 (2021), no. 3 (Shokurov’s 70th birthday volume), 157-174.
42. Uniqueness of the minimizer of the normalized volume function (with Ziquan Zhuang). Camb. J. Math. 9 (2021), no. 1, 149-176.
43. On properness of K-moduli spaces and optimal degenerations of Fano varieties (with Harold Blum, Daniel Halpern-Leistner and Yuchen Liu). Selecta. Math. (N.S.) 27(2021), no. 4, Paper No. 73.
44. Algebraicity of the Metric Tangent Cones and Equivariant K-stability (with Chi Li and Xiaowei Wang). J. Amer. Math. Soc. 34 (2021) no. 4, 1175-1214.
45. Lagrangian fibrations of hyperkähler fourfolds (with Daniel Huybrechts). J. Inst. Math. Jussieu 21 (2022) no. 3, 921-932.
46. Finite generation for valuations computing stability thresholds and applications to K-stability (with Yuchen Liu and Ziquan Zhuang). Annals of Math. 196 (2022), Issue 2, 507-566.
47. Openness of K-semistability for Fano varieties (with Harold Blum and Yuchen Liu). Duke Math. J. 171 (2022), Issue 13, 2753-2797.
2023-
48. The existence of the Kähler-Ricci soliton degeneration. (with Harold Blum, Yuchen Liu and Ziquan Zhuang). Forum Math. Pi 11 (2023), Paper No. e9.
49. K-stability for varieties with a big anti canonical class. Épijournal Géom. Algébrique, Special volume in Honour of C. Voisin, (2023) Article No. 7.
50. Stable degenerations of singularities (with Ziquan Zhuang). J. Amer. Math. Soc. 38 (2025), no. 3, 585-626.
51. A note on Kollár valuations (with Yuchen Liu). To appear in Sci. China. Math., Special Issue on Algebraic Geometry.
52. Irreducible symplectic varieties with a large second Betti number (with Yuchen Liu, Zhiyu Liu). To appear in J. Reine Angew. Math..
Under Refereeing
• Boundedness of log Fano cone singularities and discreteness of local volumes (with Ziquan Zhuang).
Survey
1. Boundedness of varieties of log general type (with Christopher Hacon and James McKernan). Algebraic Geometry: Salt Lake City 2015, 309-348, Proc. Sympos. Pure Math., 97 Part 1, Amer. Math. Soc., Providence, RI, 2018.
2. Interaction between singularity theory and the minimal model program. Proceedings of the International Congress of Mathematicians-Rio de Janeiro 2018. Vol. II. Invited lectures, 807–830, World Sci. Publ., Hackensack, NJ, 2018.
3. A guided tour to normalized volumes (with Chi Li and Yuchen Liu). Geometry Analysis, In Honor of Gang Tian's 60th Birthday. Progress in Mathematics 333, 167-219, Birkhuser/Springer, Cham, 2020.
4. K-stability of Fano varieties: an algebro-geometric approach. EMS Surv. Math. Sci. 8 (2021), no.1, 265-354.
5. 法诺簇的代数K-稳定性理论 (pdf in Chinese)
6. K-stability: the recent interaction between algebraic geometry and complex geometry. Notices Amer. Math. Soc. 69 (2022), no.7, 1126-1136.
Book
1. Higher dimensional algebraic geometry-a volume in honor of V.V. Shokurov (edited with Christopher Hacon). London Math. Soc. Lecture Note Ser. 489. Cambridge University Press, Cambridge, 2025, xvi+440.
2. K-stability of Fano varieties. New Mathematical Monograph, 50. Cambridge University Press, Cambridge, 2025, xi+411 pp.