- Homology and homotopy groups of Hawiian earrings and its generalization to higher dimension.
- Barratt-Milnor Conjecture on Anamolous behaviour of singular homology.
- Fundamental groups of some complicated one - dimensional spaces such as Hawaiian earring, Menger curve, Sierpinski curve etc.,.
- Non-metrizable manifolds such as Long Line and its generalization to higher dimensions.
Harishchandra Research Institute (HRI), Allahabad, India (Awarded by : R. D. University, Jabalpur), July 2008
- IISER Fellow, IISER Kolkata (March 2010 --Till Date)
- Visiting Scientist, Harishchandra Research Institute (HRI), Allahabad. (December 2009 -- March 2010)
- Postdoctoral Fellow, Institute of Mathematical Sciences (IMSc.) Chennai (December 2007 -- December 2009)
- Visiting Fellow, Institute of Mathematical Sciences (IMSc.) Chennai (August 2007 -- December 2007)
- ”Torsion subgroups of the homeomorphism groups of products of long line”, with P. Sankaran. "Topology and its Applications" 158, Vol. 9, (2011) pp. 1136-1139
- “An Inverse system of nonempty objects with empty limit”, with Satya Deo (http://arxiv.org/abs/0908.2168v1) "Indian Jour. of Math". 51 no 3 (2009) pp 689-697.
- “Strongly Contractible Polyhedra which are not Simply Contractible at n Points for any n ≥ 2”, with Satya Deo,"Jour. Indian Math. Soc." 72,(2005) pp.75-82.