### Algebra

Algebra is one of the core areas in Mathematics. In addition to its fundamentals, the subject of algebra also has strong connections to several other areas of mathematics like algebraic topology, algebraic geometry, operator theory, knot theory, theoretical physics and quantum theory. It has wide applications in many areas including coding theory, cryptography, Network analysis, spectral graph theory, mathematical physics, computer algorithms, to name a few!

At present, Prof. Amber Habib, Prof. A. Satyanarayana Reddy and Dr. Neha Gupta are members of this group. The main areas of interest of the group lie in Algebraic Graph Theory, Combinatorial matrix theory,

Algebraic Number Theory, Integer Partition Theory, Category Theory, Homological Algebraic Topology, and Algebraic Combinatorics. Python, Sage, Mathematica and Wxmaxima are a few softwares used in their research.

A few key areas of research are in category theory, polynomials divisible by cyclotomic polynomials, Ramanujan sums, circulant matrices, circulant graphs, applications of Ramanujan sums and circulant matrices in signal processing and image processing, exponents of nonnegative matrices, arithmetic functions, total positivity of matrices which arise from combinatorics and post-quantum cryptography. Few of these works are in collaboration with electrical engineering and computer science engineering.