Preprints and Publications (in the order they appeared on arXiv)

  1. Minimal slopes and bubbling for complex Hessian equations (with Ramesh Mete and Jian Song), arXiv link.
  2. Diameter rigidity for Kähler manifolds with positive bisectional curvature (with Harish Seshadri), Math. Ann. Volume 385, pages 471–479 (2023), journal link , arXiv link.
  3. Kähler-Einstein metric near an isolated log canonical singularity (with Xin Fu and Jian Song), to appear in J. Reine Angew. Math. (Crelle's journal), journal link (online first) arXiv link.
  4. Metric rigidity of Kähler manifolds with lower Ricci bounds and almost maximal volume (with Harish Seshadri and Jian Song), Proc. of the AMS, 149 (2021), no. 8, 3569–3574 journal link , arXiv link.
  5. A numerical criterion for generalised Monge-Ampere equations on projective manifolds (with Vamsi Pingali), Geom. Func. Anal. (GAFA), 31 (2021), no. 4, 767--814, journal link, arXiv link.
  6. On coupled constant scalar curvature Kähler metrics (with Vamsi Pingali), J. Symplectic Geom., 18 (2020), no. 4, 961–994, journal link , arXiv link.
  7. Adiabatic limits of anti-self-dual connections on collapsed K3 surfaces (with Adam Jacob and Yuguang Zhang), J. Differential Geom., 118 (2021) 223-296. journal link , arXiv link.
  8. Hermitian-Yang-Mills connections on collapsing elliptically fibered K3 surfaces (with Adam Jacob), J. Geom. Anal., 32, Article - 69 (online only), journal link, arXiv link.
  9. Expansions of solutions to extremal metric type equations on blow-ups of cscK surfaces, Ann. Global Anal. Geom., 55 (2019), no. 2, 215–241, journal link , arXiv link.
  10. Kähler-Einstein metrics along the smooth continuity method (with Gábor Székelyhidi), Geom. Funct. Anal. (GAFA), 26 (2016), no. 4, 975--1010, journal link, arXiv link.
  11. On convexity of the regular set of conical Kähler-Einstein metrics, Math. Res. Lett., 23 (2016), no. 1, 105--126, journal link, arXiv link.
  12. A remark on Kähler metrics with conical singularities along a simple normal crossing divisor (with Jian Song), Bull. Lond. Math. Soc., 47 (2015), no. 6, 1010--1013, journal link, arXiv link.
  13. Connecting toric manifolds by conical Kähler-Einstein metrics (with Bin Guo, Jian Song and Xiaowei Wang), Advances in Math., 323 (2018), 38-83, journal link, arXiv link.

Surveys and expository articles

  • Comparison and Rigidity Theorems for the Volume and Diameter of Positively Curved Kähler Manifolds (with Harish Seshadri), Acta Mathematica Sinica, English Series Published online: December 13, 2024 https://doi.org/10.1007/s10114-024-3479-1 journal link
  • An overview of the work of Karen Uhlenbeck (with Agnid Banerjee), The Mathematics Consortium Bulletin July 2020 Vol. 2, Issue 1 journal link

    • Videos of some select talks

  • Minimal slopes and singular solutions for complex Hessian equation
    • INI, Cambridge, UK, May 2024.

  • Moment maps and canonical metrics in complex geometry
    • Virtual Math Fest July 2020.

    Slides of some select talks

  • Kahler-Einstein metrics along the smooth continuity methods
    • IISc, January, 2018.

  • (Inverse) Hessian equations and positivity conditions in Kahler geometry
    • CMI alumini talks (webinar), June, 2020.

    Notes

  • AIS IISc July, 2019 - Lecture notes on Calabi's conjectures and Kahler-Einstein metrics