Mathematics

Research Interest:

1. Combinatorial and Homological Methods in Commutative Algebra and Algebraic Geometry: I study Castelnuovo-Mumford Regularity, Depth, Projective Dimensions and Betti Numbers of various powers, symbolic powers and integral closures of powers of homogeneous ideals in polynomial rings. I also study various containment relations between ordinary and symbolic powers. I have a special interest in ideals related to graphs like edge ideals, path ideals, binomial edge ideals etc. In my PhD thesis I developed a method to study homological algebra of powers of edge ideals. For symbolic powers I'm interested in characterising the packing problem and recently solved it for three path ideals in a joint work. Recently I have started studying and working on Hilbert-Kunz multiplicities and other topics in characteristic p methods.

2. Application of Algebra, Combinatorics and Statistical Machine Learning in Medical Bioinformatics: I study algebra and combinatorics of various immunological and cancer networks with an eye to find new drug targets. For large networks I seek to use Statistical Machine Learning techniques to improve existing computer algebra tools. Recently using algebraic analysis of immunological networks me and my collaborators predicted that common RA medicine Baricitinib can be useful to treat COVID infected patients.