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.

All Publications

Edge ideals of Erd s Rényi random graphs: linear resolution, unmixedness and regularity by Banerjee A., D Y. Journal of Algebraic Combinatorics 58 1125-1154 (2023)
Equality of ordinary and symbolic powers of edge ideals of weighted oriented graphs by Banerjee A., Chakraborty B. , Das K. K., Mandal M. , S S. Communications in Algebra 51 - (2023)
Bounds for Regularity of Products of Edge Ideals by Banerjee A., Selvaraja S. , Das P. ALGEBRAIC COMBINATORICS - (Accepted/In-Press)
Linear resolution of products of monomial ideals related to maximal minors by Banerjee A., Ghosh D. , Selvaraja S. Journal of the Ramanujan Mathematical Society 41 1-8 (2026)
Integral closures of powers of sums of ideals by Banerjee A., Ha T. H. Journal of Algebraic Combinatorics 58 307-323 (2023)
Integral Closure of Powers of Edge Ideals of Weighted Oriented Graphs by Banerjee A., Das K.K., Haque S. Acta Mathematica Vietnamica 50 33-49 (2025)
On Obtaining New MUBs by Finding Points on Complete Intersection Varieties over by Banerjee A., Das K.K., Kumar A., Kumar R., Maitra S. International Journal of Theoretical Physics 64 - (2025)
Ordinary and Symbolic Powers of Edge Ideals of Weighted Oriented Graphs by Banerjee A., Das K.K., Selvaraja S. Bulletin of the Malaysian Mathematical Sciences Society 48 - (2025)
Ratliff Property of Edge Ideals of Weighted Oriented Graphs by Banerjee A., Das K.K., Roy P. Electronic Journal of Combinatorics 32 - (2025)
ON THE HILBERT-SAMUEL COEFFICIENTS OF FROBENIUS POWERS OF AN IDEAL by Banerjee A., Goel K., Verma J.K. Proceedings of the American Mathematical Society 152 1501-1515 (2024)