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.

This Fall, I am entering the JOB MARKET.

To be updated soon.

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

• We are investigating some Rational Powers of an Ideal [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]