My primary research interest concerns the understanding and analysis of complex network systems and quantum systems, in which, matrix theory/computations plays an important role. I primarily work on theory and numerical algorithms for problems involving structured matrices.
Many real world systems can be viewed as systems of interconnected systems. These systems can be considered as networks, the vertices represent individual systems and edges manifest dependencies between the systems. Often, these edges in a real network are known but dynamic or not known. This half-known dependencies contribute to complexities in understanding the conduct of the entire system. Networks can be represented by (structured) matrices and hence properties of these matrices become increasingly important for the analysis of the corresponding network systems.
The phenomena of entanglement in multipartite quantum mechanical systems has no classical analogue. In general, measures of quantum correlations of multipartite systems is an exciting topic in quantum information and computation. I am interested in such problems for mixed states which are represented by especially structured matrices.
Periodicity of lively quantum walks on cycles with generalized Grover coin by Sarma Sarkar R., Mandal A. , Adhikari B. Linear Algebra and its Applications 604 399-424 (2020)
Construction of cospectral graphs by Dutta S., Adhikari B. Journal of Algebraic Combinatorics 52 215-235 (2020)
A diffusion protocol for detection of link failure and utilization of resources in multi-agent systems by Pandey P. K., Adhikari B. , Chakraborty S. IEEE Transactions on Network Science and Engineering 7 1493-1507 (2020)
Self-organized corona graphs: a deterministic complex network model with hierarchical structure by Sharma R., Adhikari B. , Krueger T. Advances in Complex Systems 22 1950019- (2019)
Condition for zero and nonzero discord in graph Laplacian quantum states by Dutta S., Adhikari B. , Banerjee S. International Journal of Quantum Information 17(02) - (2019)
Md Aminur Hossain
Area of Research: Quantum Graphs
Area of Research: Applied Linear Algebra
Area of Research: Matrix Theory
Area of Research: Citation Networks
Area of Research: Computational Linear Algebra
Rohit Sarma Sarkar
Area of Research: Quantum Computing