Brahadeesh Sankarnarayanan

Welcome to my homepage!

I am an Assistant Professor (Grade II) in the Department of Mathematics at IIT Jodhpur. My current research interest is in extremal graph theory and combinatorics.

I completed my BS-MS (Dual) Degree programme with a major in Mathematics from IISER Bhopal in 2017. I defended my PhD thesis in Combinatorics from IIT Bombay in 2024. I was an Institute Post-Doctoral Fellow at the same institute until February 2025, and I was a Research Associate at IIT Hyderabad until September 2025.

Please take a look around this website to know more about me.

Research work

At IIT Hyderabad, I worked with M. Rajesh Kannan on Brualdi–Hoffman-type extremal problems in spectral graph theory.

The classical extremal Turán-type problem asks for bounds on the number of edges of an F-free graph on n vertices, and a characterization of the graphs that attain the bound, where F is a fixed graph (or a class of graphs). The spectral version of this problem, introduced by Nikiforov, asks for bounds on the maximum spectral radius of an F-free graph on n vertices. One can also ask analogous extremal questions for F-free graphs on m edges, and this is called a Brualdi–Hoffman-type problem. Several interesting results have recently appeared in the literature in this area; even the case when F is a triangle has been paid a great deal of attention. Our focus is on the next non-trivial case, that is, when F is the complete graph on four vertices.

During my PhD at IIT Bombay, I worked under Niranjan Balachandran in extremal graph theory and combinatorics.

In graph theory, I studied the gap between the chromatic and list chromatic numbers for graphs embeddable on a surface; in particular, I completed the classification of the colorability of the 6-regular triangulations of the torus, and found a linear-time 5-list-coloring algorithm for a large class of these triangulations.

In extremal set theory, I studied a fractional variant of L-intersecting set systems, and made significant progress on finding tight upper bounds on the sizes of such families. I also worked on computing the ranks of a class of symmetric, zero-diagonal matrices arising from these families; in particular, I showed that these matrices naturally arise as a class of generalized adjacency matrices of tournaments over [n], and that they are all of high rank (i.e., at least linear in n) with high probability.

Link to my PhD thesis: Some problems in combinatorics: Excursions in graph colorings and extremal set theory

Prior to joining my PhD, I briefly worked as a project assistant under Kumar Balasubramanian at IISER Bhopal, where I studied a small amount of p-adic representation theory.

My Master's thesis is on automorphic forms and Tate's thesis, and I was guided by Karam Deo Shankhadhar. During my undergraduate studies, I also explored some number theory under Brundaban Sahu.