Research Interests

• Arithmetic Geometry

• Additive Number Theory

• Combinatorial Group Theory

• Spectral Graph Theory and Expanders

Publications and Preprints

Arithmetic Geometry

• • The density of ramified primes. Doc. Math. 24 (2019), 2423--2429 link

  • Distinguishing pure representations by normalized traces (with Manish Kumar Pandey and Sudhir Pujahari). J. Number Theory 195 (2019), 217--225 link

  • Conductors in p-adic families. Ramanujan J. 44 (2017), no. 2, 359--366 link

  • Purity for families of Galois representations. Ann. Inst. Fourier (Grenoble) 67 (2017), no. 2, 879--910 link

  • Congruences of algebraic L-functions of motives (with Olivier Fouquet) link

  • Variation of Weyl modules in p-adic families link

  • An algebraic p-adic L-function for p-adic families link

  • On Frobenius semisimplicity in Hida families link

  • On some local properties of sequences of big Galois representations (with S. Aniruddha). J. Number Theory 264 (2024), 295--306 link

Additive Number Theory

• • Minimal additive complements in finitely generated abelian groups (with Arindam Biswas). Ramanujan J. 57 (2022), no. 1, 215--238 link

  • Asymptotic complements in the integers (with Arindam Biswas). J. Number Theory 213 (2020), 101--115 link

  • Infinite co-minimal pairs in the integers and integral lattices (with Arindam Biswas). Combinatorial and additive number theory. IV, Springer Proc. Math. Stat., vol. 347, Springer, 2021, 41--71 link

  • Infinite co-minimal pairs involving lacunary sequences and generalisations to higher dimensions (with Arindam Biswas). Ramanujan J. 57 (2022), no. 4, 1445--1462 link

Combinatorics on Groups

• • On minimal complements in groups (with Arindam Biswas). Ramanujan J. 55 (2021), no. 3, 823--847 link

  • On additive co-minimal pairs (with Arindam Biswas). J. Number Theory 223 (2021), 350--370 link

  • On non-minimal complements (with Arindam Biswas). Adv. in Appl. Math. 130 (2021), Paper no. 102226, 25 pp.  link

  • Asymptotic behaviour of minimal complements (with Arindam Biswas) link

  • On the cop number and the weak Meyniel's conjecture for algebraic graphs (with Arindam Biswas). European J. Combin. 128 (2025), Paper no. 104168, 17 pp.  link

Spectra of graphs and Expanders

• • A Cheeger type inequality in finite Cayley sum graphs (with Arindam Biswas). Algebr. Comb. 4 (2021), no. 3, 517--531 link

  • Spectral bounds of directed Cayley graphs of finite groups (with Arindam Biswas). Israel J. Math. 249 (2022), no. 2, 973--998 link

  • Spectra of twists of Cayley and Cayley sum graphs (with Arindam Biswas). Adv. in Appl. Math. 132 (2022), Paper no. 102272, 34 pp. link

  • Expansion in Cayley graphs, Cayley sum graphs and their twists (with Arindam Biswas) link

  • A spectral bound for vertex-transitive graphs and their spanning subgraphs (with Arindam Biswas). Algebr. Comb. 6 (2023), no. 3, 689--706 link

  • A Cheeger inequality for the lower spectral gap. link

Word maps

• • On non-surjective word maps on PSL_2(F_q) (with Arindam Biswas) Arch. Math. (Basel) 122 (2024), no. 1, 1--11 link