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Research Interests : I am interested in differential geometry and geometric analysis. Specifically, I work on manifolds with special holonomy. More specifically, I work on manifolds with G2 or Spin(7) structure.

I think about :

  • General flows of G2 or Spin(7) structures.
  • Laplacian flow for closed G2 structures.
  • Calibrated submanifolds or more generally, minimal submanifolds of G2 or nearly G2 manifolds.
  • Construction of torsion-free compact examples of manifolds with a G2 or Spin(7) structures.
  • Some problems in Metric geometry.

Publications :

Research Papers and Preprints (arXiv, ORCiD, zbMATH)


14. Ricci flow with metric torsion on surfaces of positive Euler characteristic. [arXiv]

13. A ddΦ-Lemma and Bott--Chern-type Cohomology for Spin(7)-Manifolds (with Ragini Singhal), submitted. [arXiv]

12. Solutions and singularities of the Ricci-harmonic flow and Ricci-like flows of G2-structures (with Ragini Singhal), submitted. [arXiv]

11. Ricci-harmonic flow of G2 and Spin(7)-structures, submitted. [arXiv]

10. A gradient flow of Spin(7)-structures, Quarterly Journal of Mathematics, Volume 76, Issue 2, June 2025, Pages 537–563. [journal][arXiv]

9. Flows of G2 structures Ⅱ: Curvature, torsion, symbols and functionals (with Panagiotis Gianniotis and Spiro Karigiannis), Pure and Applied Math Quarterly Volume 21 (2025) Number 5. [journal][arXiv]

8. Some results on almost *-Ricci-Bourguignon solitons (with Dhriti Sundar Patra), Journal of Geometry and Physics, 178 (2022). [journal]

7. Associative submanifolds in Joyce’s generalised Kummer constructions (with Daniel Platt and Thomas Walpuski), Communications in Mathematical Physics, 401 (2023). [journal][arXiv]

6. Harmonic flow of Spin(7)-structures (with Eric Loubeau and Henrique Sá Earp), Ann. Sc. Norm. Super. Pisa Cl. Sci, Vol. XXV (2024), 151-215. [journal][arXiv]

5. Deformation theory of nearly G2 manifolds (with Ragini Singhal), Communications in Analysis and Geometry, Volume 31 Number 3 2023. [journal][arXiv]

4. A gradient flow of isometric G2 structures (with Panagiotis Gianniotis and Spiro Karigiannis), Journal of Geometric Analysis, 31, 1855–1933 (2021). [journal][arXiv]

3. Some results on Ricci-Bourguignon and Ricci-Bourguignon almost solitons, Canadian Mathematical Bulletin, (2020). [journal] [arXiv]

2. Minimal Hypersurfaces in Nearly G2 manifolds, Journal of Geometry and Physics , 135C (2019), 253-264. [journal][arXiv]


Book :

1. Hamiltonian group actions and Equivariant cohomology (with Jon Herman, Lisa Jeffrey, and Theo van den Hurk), SpringerBriefs in Mathematics (2019). [Book]

Thesis :

Topics in G2 geometry and geometric flows, PhD thesis, University of Waterloo (2020). [Thesis]