I am an Assistant Professor in the Discipline of Computer Science & Engineering, IIT Indore

“Everybody understood that if the proof is correct, then no other recognition is needed”- Grigori Perelman (The mad monk of maths)

I have a huge regard for mathematics (the queen of sciences), and mathematicians (I am very far from being one). They are the best contributor to humanity, often silent yet elegant, they are always well ahead of the present time, the world follow them later. They have their own challenges and frustration nicely explained by mathematician RB Bapat.

# Research Interests

I broadly work in spectral graph theory, that is, the study of graphs using the matrices associated with graphs like adjacency matrix, Laplacian matrix, Seidel matrix, etc. The two problem I am primarily interested in are

- the constructions of the expander graphs and in particular explicit construction of Ramanujan graphs which are the best possible expanders.
- For more detail see an excellent survey by Hoory, Linial, Wigderson

- matrix determinant (P) vs matrix permanent (#P-complete) problem.
- For more detail see articles by Manindra Agrawal and Frank Ban

**For the students who want to work with me:** please drop me an email if your are interested in the following reasearch areas: *Algorithmic Graphs (Matrix) Theory, Computational Complexity, Complex network analysis*.

# Ongoing project under me

- Reducing parameterized complexities of matrix determinant and permanents.
- Construction of expanders and Ramanujan graphs for fast network topologies.

For some open problem proposed by me see Mathoverflow. For some interesting read and ideas see Medium.

# Contact Address:

Room No. 408 POD 1A, IIT Indore

Contact: +91-731-6603224

Indore-453552, MP, India