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1. Constructing Certain Special Analytic Galois Extensions

11F80; J. Number theory (2020) Vol. 212, pp. 105-112 (journal version).

2. Euler Characteristics and their Congruences in the Positive Rank setting

11R23; joint with Ramdorai Sujatha,

Canadian Math. Bull. (2021) Vol. 64, no. 1, pp. 228-245 (journal version).


3. On Picard Groups of Perfectoid Covers of Toric varieties

14G45; joint with Gabriel Dorfsman-Hopkins and Peter Wear,

European J. of Mathematics (2023) Vol. 9,  issue 1, article 16. (journal version).

4. Euler Characteristics and their Congruences for Multi-signed Selmer groups

11R23; joint with Ramdorai Sujatha,

Canadian J. of Mathematics (2023) Vol. 75(1),  pp. 298-321.(journal version).

5. A Refined Lifting Theorem for Supersingular Galois Representations

11F80; J. Number theory (2021) Vol. 229, pp. 282-313 (journal version).

6. Constructing Galois Representations Ramified at One Prime

11F80; J. Number theory (2021) Vol. 222, pp. 168-180 (journal version).

7. Deformations of Certain Reducible Galois Representations III

11F80; Int. J. Number theory (2021) Vol. 17, Issue 06 pp. 1429-1485 (journal version).

8. Anticyclotomic μ-invariants of residually reducible Galois Representations

11R23; joint with Debanjana Kundu,

J. Number theory (2022) Vol. 234, pp. 476-498 (journal version).

9. Iwasawa Invariants for Elliptic Curves over Zp-extensions and Kida's formula

11R23; joint with Debanjana Kundu.

Forum Math. 34 (2022), no. 4, 945–967 (journal versionLink to auxiliary code).

10. Deformations of Reducible Galois Representations to Hida Families

11F80; Int. J. Number theory (2022) Vol. 18, No. 01, pp. 89-112 (journal version).

11. On the μ-invariants of residually reducible Galois representations

11F80, 11R23; preprint (April 2021), joint with Ramdorai Sujatha.

accepted for publication in the American J. of Mathematics

12. Constructing Galois Representations with large Iwasawa λ-invariant

11F80, 11R23; Annales Math. Quebec 48 (2024), no. 1, 253–268. (journal version)

13. Statistics for Iwasawa Invariants of Elliptic Curves

11R23; joint with Debanjana Kundu,

Trans. American Math. Soc. (2021) Vol. 374, no.11, pp. 7945-7965 (journal version).

14. Statistics for Anticyclotomic Iwasawa Invariants of Elliptic Curves

11R23; joint with Jeffrey Hatley and Debanjana Kundu.

 Math Zeitschrift : (2024), Vol 307, no. 3, Paper No. 49. (journal version)

15. Statistics for Iwasawa Invariants of Elliptic Curves, II

11R23; joint with Debanjana Kundu

Int. J. Number theory Volume 20, Issue 04 (May 2024), pp.1099-1124 (journal version)

16. Rank Jumps and Growth of Shafarevich-Tate groups of Elliptic curves in Z/pZ-extensions; 11G05, 11R23; joint with Lea Beneish and Debanjana Kundu.

 J. Australian Math. Soc. 116 (2024), no. 1, 1–38. (journal version)

17. Arithmetic Statistics for Galois Deformation Rings

11G05, 11F80; joint with Tom Weston.

The Ramanujan Journal  (2024), no. 3, pp. 685-708

18. Arithmetic Statistics and Diophantine Stability for Elliptic curves

11G05, 11R23; The Ramanujan Journal (2023), 62, pp. 215–239  (journal version)

19. Asymptotic Growth for Mordell-Weil Ranks of Elliptic curves in Noncommutative Towers

11G05, 11R23; Canadian Math. Bull. (2022), 65(4), pp. 1050-1062. (journal version).

20. Arithmetic Statistics and Noncommutative Iwasawa theory

11G05, 11R23; joint with Debanjana Kundu and Antonio Lei

Documenta Math. (2022), 27, pp. 89-149 (journal version).

21. Rational points on Algebraic Curves in Infinite towers of Number fields

11G10, 11G30, 11R23; The Ramanujan Journal (2023), Vol. 60, pp. 809–824. (journal version).

22. Statistics for p-ranks of Artin-Schreier covers

11G20; Acta Arithmetica 205 (2022) , 211-226 (journal version).

23. Iwasawa Invariants for Symmetric Square representations

11R23; joint with Ramdorai Sujatha and Vinayak Vatsal

Research in the Mathematical Sciences (2023), Vol 10, issue 1, 27. (journal version)

24. Arithmetic Statistics for the Fine Selmer group in Iwasawa theory

11G05, 11R23; joint with Ramdorai Sujatha

Research in Number theory (2023), Vol 9, issue 3, 59. (journal version)

25. On the μ equals zero conjecture for the Fine Selmer group in Iwasawa theory

11F80, 11G05, 11R23; joint with Shaunak Deo and Ramdorai Sujatha

Pure & Applied Math. Quarterly (2023) vol.19, no.2, pp. 641-680 (journal version)

26. Topological Iwasawa invariants and Arithmetic Statistics

11R23, 57K10; joint with Cedric Dion

Documenta Math. (2022), 27, pp. 1643-1669; (journal version).

27. Class group statistics for torsion fields generated by elliptic curves

11G05; preprint (April 2022), joint with Tom Weston

28. Asymptotic growth of Iwasawa invariants in Noncommutative towers of number fields

11R23; preprint (June 2022).

29. Remarks of Hilbert's tenth problem and the Iwasawa theory of elliptic curves

11R23, 11G05, 11U05;

Bull. Australian Math. Soc. (2023), 107(3), pp. 440-450 (journal version)

30. Remarks on Catalan's equation over Function fields

11D41, 11R58;

Finite Fields & their Applications (2023), Vol. 91, no. 102271 (journal version)

31. Diophantine equations of the form Y^n=f(X) over function fields

11D41, 11R58;

Bull. Australian Math. Soc. 108 (2023), no. 3, pp. 379–390.  (journal version)

32. On the distribution of Iwasawa invariants associated to Multigraphs

05C25, 11R23; joint with Cedric Dion,  Antonio Lei and Daniel Vallieres.

Nagoya Math. J108Volume 253, (2024) , pp. 48 - 90 (journal version)

33. A note on the distribution of Iwasawa invariants of imaginary quadratic fields

11R23;  Bull Braz Math Soc (2023), New Series 54, 36. (journal version)

34. On large Iwasawa λ-invariants of imaginary quadratic function fields

11R23; The Ramanujan Journal (2023), Vol. 62, pp. 853-861 (journal version)

35. On the corank of the fine Selmer group of an elliptic curve over a Zp-extension

11R23, 11G05; the Ramanujan Journal Vol. 62 (2023), no. 4, 1023–1035.(journal version)

36. An analogue of Kida's formula in graph theory

05C25, 11R23; preprint  (Sep 2022),  joint with Daniel Vallieres.

37. Galois representations ramified at one prime and with suitably large image

11F80;Trans. American Math. Soc. (2023) Vol. 376 No.10, pp. 7287-7305 (journal version)

38. On the number of subrings of  Z^n of prime power index

11H06, 11A25; preprint (Nov 2022), joint with Hrishabh Mishra

39. On the distribution of Alexander polynomials in certain families of closed braids

11R29, 57M25;

European J. of Mathematics (2023) Vol 9, Issue 3, article 65 (journal version)

40. Hilbert's tenth problem in anticyclotomic towers of number fields

11R23, 11U05; joint with Tom Weston

Trans. American Math. Soc. (2024) Vol. 377, No. 5, pp. 3577-3597 (journal version)

41. Constructing Galois representations with prescribed Iwasawa λ-invariant

11R23, 11F80; 

Bulletin of the London Math. Soc. (2024) Vol. 56, Issue. 5, pp. 1624-1642 (journal version)

42. On the distribution of eigenvalues in families of Cayley graphs

11H06, 05C25; preprint (Mar 2023); joint with Matilde Lalin

European J. of Mathematics: revisions

43. Diophantine stability for elliptic curves on average

11GO5, 11U05, 11R45; preprint (April 2023), joint with Tom Weston

44. Lower bounds for the number of number fields with Galois group GL2(Fℓ)

11R32, 11G05; preprint (May 2023).

45. Counting number fields whose Galois group is a wreath product of  symmetric groups joint with Hrishabh Mishra, 11R45, 11R29, 37P15; preprint (June 2023).

46. Remarks on Greenberg's conjecture for Galois representations associated to elliptic curves , 

11R23; preprint (August 2023).

47. Asymptotic growth patterns for class field towers ,

 11S20, 11R23; joint with Arindam Bhattacharyya  and Vishnu Kadiri, 

Documenta Math. 29 (2024), no. 1, 141–158 (journal version).

48. On the Iwasawa invariants of Artin representations11R23, 11F80;

preprint (September 2023), joint with Aditya Karnataki

49. Upper bounds on the number of number fields with prescribed Galois group11R45, 11R29; preprint (October 2023), joint with Hrishabh Mishra

50. Iwasawa theory of fine Selmer groups associated to Drinfeld modules 

11R23, 11G09, Mathematika (2024) Volume70, Issue3 (journal version)

51. The T-adic Galois representation is surjective for a positive density of Drinfeld modules 

11F80, 11G09, Research in Number theory: Vol 10, No. 56 (2024) (journal version)

52. Rank stability of elliptic curves in certain metabelian extensions, preprint (Jan 2024) joint with Siddhi Pathak11R45, 11G05

53. On Malle's conjecture for the product of symmetric and nilpotent groups, preprint (Feb 2024) joint with Hrishabh Mishra, 11R45, 11R32. Nagoya Math. J : revisions

54. An analogue of Kida's formula for elliptic curves with additive reduction preprint (Feb 2024) joint with Pratiksha Shingavekar, 11R23, 11G05. 

accepted for publication in the The Ramanujan Journal

55. Rank distribution in cubic twist families of elliptic curves preprint (Mar 2024) joint with Pratiksha Shingavekar, 11G05, 11R45, 11R34.

56.Statistics for Iwasawa Invariants of Elliptic Curves, III preprint (Apr 2024) 11R23, 11R45

57.On the Iwasawa theory of Cayley graphs preprint (May 2024) joint with Sohan Ghosh, 11R23, 05C25

58. Hilbert's tenth problem for families of Zp-extensions of imaginary quadratic fields joint with Katharina Müller, preprint (June 2024) 11R23, 11U05, 11G05

59. Galois representations over function fields that are ramified at one prime, preprint (June 2024) 11F80, 11G09.

60. A positive density of elliptic curves are diophantine stable in certain Galois extensions, joint with Pratiksha Shingavekar,  preprint (June 2024), 11R45, 11G05, 11R32.

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