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 H. 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, 73 (39 pages).
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.
Under Refereeing
• Stable degenerations of singularities (with Ziquan Zhuang).
• A note on Kollár valuations (with Yuchen Liu).
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.