Research
Accepted
Cheeger Inqualities for Graph Limits, 2018 (with Mahan Mj) (Annales de l'Institut Fourier) [arXiv]
Improved Upper Bound for the Size of a Trifferent Code, 2024 (with Siddharth Bhandari) (ISIT 2024) [arXiv]
Preprints
A Periodicity Result for Tilings of Z^3 by Clusters of Prime-Squared Cardinality, 2021 [arXiv]
A Ramsey Theorem for Graded Lattices, 2021 (with Amitava Bhattacharya) [arXiv]
On Configurations of Order 2, 2021 [arXiv]
Theses
August 2016 - August 2021 (PhD Theses in Mathematics at TIFR)
Thesis Title: Geometric and Analytic Methods in Combinatorial Problems.
Thesis Advisor: Prof. Mahan Mj.
Brief Description: The Thesis comprises three pieces of work. We prove Cheeger inequalities for graph limits and show that the classical Cheeger inequalities for finite graphs cab be recovered from the graph limit version of the same. Then we prove a natural generalization of the van der Waerden theorem in Ramsey theory in the setting of graded lattices and recover the Hales-Jewett theorem as a corollary of our main theorem. Lastly, we discuss a periodicity result about configurations of order 2.
August 2015 - April 2016 (Masters Thesis in Mathematics at CMI)
Project Title: A Cellular Model for Configuration Spaces of Points on a Graphs. [Thesis]
Project Guide: Prof. Priyavrat Deshpande.
Brief Description: A lot of work has been done in understanding the homotopy types of configuration spaces. Recently, Dai Tamaki has come up with a suitable cell structure for these spaces. Moreover, this cell structure is combinatorially determined. The thesis is a survey of Tamaki's work and its application to configuration spaces of points on a graph.
July 2013 - April 2014 (Masters Thesis in Mechanical Engineering at IIT Kharagpur)
Project Title: On the Generalization of Rigidity and Flexibility: From Tensegrity Frameworks to Arbitrary C^1 Functions [Thesis]
Project Guide: Prof. Anirvan Dasgupta, Dept. of Mechanical Engineering, IIT Kharagpur.
Brief Description: The first significant results in the mathematical study of tensegrity frameworks were published by Roth and Whiteley in the paper Tensegrity Frameworks, 1981. In this paper the authors have made precise the notions of 'rigidity' and 'flexibility' of tensegrities and proved a fundamental theorem which states that a tensegrity framework is not rigid in a configuration if and only if it is flexible in that configuration. In this thesis we have generalized the notion of rigidity and flexibility to arbitrary continuously differentiable functions and have proved an analogous result which sates that the equivalence of non-rigidity and flexibility is a generic property in this new setting.