My mathematical interests are in Commutative Algebra and its interactions with Algebraic Geometry and Combinatorics. 

A list of problems/research areas that I have worked/working so far: 

• Interpolation problems and symbolic powers of ideals: My current interest revolves around this, which associates Chudnovsky's Conjecture and Demailly's Conjecture.

• Rational powers of Ideals: A recent few papers draw my attention towards this area, and it seems interesting.

• Vasconcelos number or v-number (in honor of Wolmer Vasconcelos) of Ideals: This relatively new concept has some similar properties with the well known initial degree of an ideal, and it's growing fast.

To be updated soon.

1. Demailly's Conjecture for general and very general points. [with Sankhaneel Bisui] Submitted. [arXiv]

• We are investigating Rational powers of an Ideal and the Symbolic Powers [with Tai Ha, Souvik Dey]

• We are investigating v-numbers on Ideal defining points [with Manohar Kumar]

• We are investigating K-Configurations [with Sankhaneel Bisui]