My primary research interest concerns the understanding and analysis of complex network systems and quantum systems in which linear algebra is used as an indispensable tool. Mathematically, I research on theory and numerical algorithms for problems involving structured matrices.
Many real world systems can be viewed as systems of interconnected systems. In the language of mathematics, these systems can be considered as networks in which the nodes represent individual systems and dependencies between them can be interpreted as links which are sometimes known but dynamic or not known. This half-known behavior of dependencies contributes to complexities in understanding the behavior of the entire system. Since networks can be represented by certain structured matrices, the properties of these matrices become increasingly important for the analysis of the network systems. Thus theory and numerical algorithms for structured matrices play a significant role in solving problems arise in network systems.
In multipartite quantum systems, it is believed that the phenomena of entanglement has no classical analogue and the detection of entanglement remained an open problem for high-dimensional systems. Since quantum states are represented by density matrices (sometimes represented by a network), mathematically, it necessitates the development of new techniques for dealing with structured matrices.
Laplacian matrices of weighted digraphs represented as quantum states by Adhikari B., Banerjee S. , Adhikari S. , Kumar A. Quantum Information Processing 16 1-22 (2017)
Bipartite separability and nonlocal quantum operations on graphs by Dutta S., Adhikari B., Banerjee S. and Srikanth R. Physical Review A American Physical Society, 94 (1) 1-10 (2016)
A graph theoretical approach to states and unitary operations by Dutta S., Adhikari B. and Banerjee S. Quantum Information Processing Springer, 15 (2) 1-20 (2016)
Structured Procrustes problem by Adhikari B. and Alam R. Linear Algebra and its Applications Elsevier, 490 145-161 (2016)
Context dependent preferential attachment model for complex networks by Pandey P.K. and Adhikari B. Physica A Elsevier, 436 499-508 (2015)
Theory and Numerical Algorithms for Interval Linear System & Interval Eigen-Value Problem BRNS, DAE, MUMBAI
Md Aminur Hossain
Area of Research: Quantum Graphs
Area of Research: Applied Linear Algebra
Area of Research: Matrix Theory