ResEarch
Research Interests: The broad areas of my research interest are Differential Geometry and Geometric Analysis. In particular, I am interested in problems related to
- Ricci Flow and Curvature
- (Almost) Einstein manifolds
- Symmetric Spaces
- Riemannian Functionals
Publications:
- Some Unstable Critical Metrics for L^{n/2} -norm of the Curvature Tensor (with Soma Maity), Math. Res. Lett., 21 (2014), no. 2, 235-240.(arXiv:1211.5774)
- A gap theorem for Ricci-flat 4-manifolds (with Harish Seshadri), Differential Geom. Appl. 40 (2015), 269-277. (arXiv:1210.7488)
- On the Curvature ODE associated to the Ricci flow, Geom. Dedicata 175 (2015),189-209. (arXiv: 1310.4618)
Expository Articles:
- Hopf ’s Umlaufsatz or the Theorem of turning tangents, The Mathematics Student, Vol. 85, Nos. 3-4, July-December (2016), 105-122.
- An introductory note on the Chern-Weil Theory in vector bundles, to be published as a chapter in the book SERB School on Topology and Condensed Matter Physics.
- Lecture Notes on dynamics of the Geodesic Flow, based on a lecture series of Professor Keith Burns at TIFR-CAM, Bangalore; in March, 2015; to be published.