Address:

Mathematics Institute
University of Warwick
Coventry CV4 7AL
United Kingdom

Room : B2.34
Tel: +44 (0) 24 7657 3512
E-Mail: K dot Zheng at warwick dot ac dot uk

I am working on geometric analysis, the interface of various nonlinear partial differential equations and differential geometry, specially complex geometry. The analytic tools include calculus of variations, higher order geometric flows and complex Monge-Ampère equations. My current Research Interests involve regularity/singularity phenomena of geometric PDEs, existence/uniqueness of critical metrics and convergence of geometric flows.

Here is my Curriculum Vitae. An almost list of my publications is available at arXiv and MathSciNet.

Co-organise:
Junior Warwick-Imperial-Cambridge geometric analysis seminar. Queen Mary University of London, January 5-8, 2016.

Travel/Visiting

• Institut des Hautes Études Scientifiques, France, Sept.-Oct. 2018.
• Constant Scalar Curvature Metrics in Kähler and Sasaki Geometry. CIRM, France, January 15-19, 2018.
• Colloquia & Seminars. AMSS, Chinese Academy of Sciences, Beijing, December 4, 2017.
• Aarhus Differential Algebraic Geometry seminars. Centre for Quantum Geometry of Moduli Spaces, Denmark, November 7-8, 2017.
• Geometry of Manifolds. Simons Center for Geometry and Physics, USA, October 23-27, 2017.

Teaching

Teaching Responsibilities at Warwick:
2016/17 TERM 1: MA4A2 Advanced PDEs
2015/16 TERM 1: MA4A2 Advanced PDEs
At Hanover, I was a teaching assistant for
WS 2014/15, Mathematics for Engineers I
SS 2014, Mathematics for Engineers II
WS 2013/14, Mathematics for Engineers I
SS 2013, Mathematics for Engineers II
SS 2013, Global Analysis - Differential geometry
WS 2012/13, Mathematics for Engineers I

Publications and Preprints

1. Stability of Kähler-Ricci flow in the space of Kähler metrics
   Pacific J. Math. 251 (2011), no. 2, 469-497.
   ArXiv:1004.2695.
2. Stability of Calabi flow near an extremal metric
   Written in collaboration with H. N. Huang.
   Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 11 (2012), no. 1, 167-175.
   ArXiv:1007.4571.
3. The pseudo-Calabi flow
   Written in collaboration with X. X. Chen.
   J. Reine Angew. Math. 674 (2013), 195-251.
   ArXiv:1004.2663.
4. Kähler non-collapsing, eigenvalues and the Calabi flow
   Written in collaboration with H. Z. Li.
   J. Funct. Anal. 267 (2014), no. 5, 1593-1636.
   ArXiv:1309.4304.
5. Kähler metrics with cone singularities and uniqueness problem
   Current trends in analysis and its applications, 395-408, Trends Math. Birkhäuser/Springer, Cham, 2015.
   Pdf File
6. The Dirichlet and the weighted metrics for the space of Kähler metrics
   Written in collaboration with S. Calamai.
   Math. Ann. 363 (2015), no. 3, 817-856.
   ArXiv:1202.6610.
7. I-properness of Mabuchi's K-energy
   Calc. Var. Partial Differential Equations. 54 (2015), no. 3, 2807-2830.
   ArXiv:1410.1821.
8. Geodesics in the space of Kähler cone metrics, I
   Written in collaboration with S. Calamai.
   Amer. J. Math. 137 (2015), no. 5. 1149-1208.
   ArXiv:1205.0056.
9. The geodesic problem for the Dirichlet metric and the Ebin metric on the space of Sasakian metrics
   Written in collaboration with S. Calamai and D. Petrecca.
   New York J. Math. 22 (2016) 1111-1133.
   ArXiv:1405.1211.
10. Regularity scales and convergence of the Calabi flow
    Written in collaboration with H. Z. Li and B. Wang.
    J. Geom. Anal. (2017)
    ArXiv:1501.01851. 52 pages.
11. Generalized Matsushima's theorem and Kähler-Einstein cone metrics
    Written in collaboration with L. Li.
    Calc. Var. Partial Differential Equations. (2018).
    ArXiv:1511.02410. 43 pages.
12. Uniqueness of constant scalar curvature Kähler metrics with cone singularities, I: Reductivity
    Written in collaboration with L. Li.
    Math. Ann. (2017)
    ArXiv:1603.01743. 40 pages.
13. Construction of constant scalar curvature Kähler cone metrics
    Written in collaboration with J. Keller.
    Proc. Lond. Math. Soc. (2018).
    ArXiv:1703.06312. 46 pages.
14. Expansion formula for complex Monge–Ampère equation along cone singularities
    Written in collaboration with H. Yin.
    ArXiv:1609.03111. 29 pages.
15. Geodesics in the space of Kähler cone metrics, II. Uniqueness of constant scalar curvature Kähler cone metrics
    ArXiv:1709.09616. 71 pages.