My current area of research is broadly in the area of discrete subgroups of Lie groups. More especially, my recent research deals with the arithmeticity and thinness of the monodromy groups of hypergeometric differential equations,  Coxeter groups, and Lattices in semidirect product of Lie groups.

Publications

• (with S. V. Singh) Thinness of Some Hypergeometric Groups in Sp(6), Glasgow Mathematical Journal, (2024); Published Version;  (arXiv link). 

• (with J. Bajpai and S. V. Singh) Arithmeticity of Some Hypergeometric Groups,  Linear Algebra and its Applications, 661 (2023), 137-148;  Published Version;  (arXiv link).

• (with J. Bajpai, D. Dona and S. V. Singh) Symplectic Hypergeometric Groups of Degree Six,  Journal of Algebra, 575 (2021), 256-273; Published Version; (arXiv link).

• (with J. Bajpai and S. A. Thomson) Commensurability and Arithmetic Equivalence for Orthogonal Hypergeometric Monodromy Groups, Experimental Mathematics, 29 (2020), no. 2, 222-233; Published Version; (arXiv link).

• (with J. Bajpai) On Orthogonal Hypergeometric Groups of Degree Five,  Transactions of the American Mathematical Society, 372 (2019), no. 11, 7541-7572; Published Version; (arXiv link).

• Arithmeticity of Some Hypergeometric Monodromy Groups in Sp(4), Journal of Algebra, 473 (2017), 142-165; Published Version; (arXiv link).

• Orthogonal Hypergeometric Groups with a Maximally Unipotent Monodromy, Experimental Mathematics, 24 (2015), no. 4, 449-459; Published Version; (arXiv link).

• Arithmeticity of Four Hypergeometric Monodromy Groups Associated to Calabi-Yau Threefolds, International Mathematics Research Notices (IMRN),  2015 (2015), no. 18, 8874-8889; Published Version; (arXiv link).

• (with T. N. Venkataramana) Arithmeticity of Certain Symplectic Hypergeometric Groups, Duke Mathematical Journal, 163 (2014), no. 3,  591-617; Published Version; (arXiv link).

• Coxeter Groups are not higher rank Arithmetic Groups, Mathematical Research Letters (MRL),  20 (2013), no. 3, 567-580; Published Version; (arXiv link).

Preprints

• (with M. M. Radhika) Lattices in $\R^n\rtimes\SL_2(\R)$; (arXiv link). 

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To find my papers on arXiv, you may click here : arXiv.