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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), no.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

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. Stability of Valuations and Kollár Components (with Chi Li). To appear in J. Euro. Math. Soc..

34.  K-stability of cubic threefolds (with Yuchen Liu).  To appear in Duke Math. J..

35.  Uniqueness of K-polystable degenerations of Fano varieties (with H. Blum) To appear in Annals of Math..

Under Refereeing

•  Rational points of rationally simply connected varieties over global functional fields (with Jason Starr). 

•  Algebraicity of the Metric Tangent Cones and Equivariant K-stability (with Chi Li and Xiaowei Wang) 

•  Lagrangian fibrations of hyperkähler fourfolds (with D. Huybrechts)

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 ICM 2018 Vol.1 803-828.

3. A guided tour to normalized volumes (with Chi Li and Yuchen Liu).