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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)

  1. A gradient flow of Spin(7)-structures, (2024). [arXiv]

  2. Flows of G2 structures Ⅱ: Curvature, torsion, symbols and functionals (with Panagiotis Gianniotis and Spiro Karigiannis) (2023). [arXiv]

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

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

  5. 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]

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

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

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

  9. 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]