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1. Constructing Certain Special Analytic Galois Extensions

11F80J. 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; preprint (Nov 2020), joint with Gabriel Dorfsman-Hopkins and Peter Wear,

European J. of Mathematics : revisions.

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

11R23; joint with Ramdorai Sujatha,

accepted for publication in Canadian J. of Mathematics (journal version).

5. A Refined Lifting Theorem for Supersingular Galois Representations

11F80J. Number theory (2021) Vol. 229, pp. 282-313 (journal version).

6. Constructing Galois Representations Ramified at One Prime

11F80J. 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 mu-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; preprint (March 2021), 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

11F80Int. J. Number theory (2022) Vol. 18, No. 01, pp. 89-112 (journal version).

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

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

12. Constructing Galois Representations with large Iwasawa lambda-invariant

11F80, 11R23; preprint (May 2021).

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; preprint (May 2021), joint with Jeffrey Hatley and Debanjana Kundu.

15. Statistics for Iwasawa Invariants of Elliptic Curves, II

11R23; preprint (June 2021), joint with Debanjana Kundu.

16. Rank Jumps and Growth of Shafarevich-Tate groups of Elliptic curves in Z/pZ-extensions

11G05, 11R23; preprint (July 2021), joint with Lea Beneish and Debanjana Kundu.

17. Arithmetic Statistics for Galois Deformation Rings

11G05, 11F80; preprint (Aug 2021), joint with Tom Weston.

18. Arithmetic Statistics and Diophantine Stability for Elliptic curves

11G05, 11R23; preprint (Sep 2021).

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

11G05, 11R23; accepted for publication in Canadian Math. Bull. (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; accepted for publication in The Ramanujan Journal (journal version).

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

11G20; accepted for publication in Acta Arithmetica.

23. Iwasawa Invariants for Symmetric Square representations

11R23; preprint (Nov 2021), joint with Ramdorai Sujatha and Vinayak Vatsal

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

11G05, 11R23; preprint (Dec 2021), joint with Ramdorai Sujatha

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

11F80, 11G05, 11R23; preprint (Feb 2022), joint with Shaunak Deo and Ramdorai Sujatha

26. Topological Iwasawa invariants and Arithmetic Statistics

11R23, 57K10; preprint (Mar 2022), joint with Cedric Dion

Documenta Math: accepted with revisions (Link to auxiliary code).

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; preprint (June 2022).

accepted for publication in Bull. Australian Math. Soc.

30. Remarks on Catalan's equation over Function fields

11D41, 11R58; preprint (June 2022).

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

11D41, 11R58; preprint (July 2022).

32. On the distribution of Iwasawa invariants associated to Multigraphs

05C25, 11R23; preprint (July 2022), joint with Cedric Dion,  Antonio Lei and Daniel Vallieres.

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MSC Subject classes:

11D41: Diophantine equations of higher degree;

Fermat's equation

11G05: Elliptic curves over Global fields

11G10: Abelian varieties of dimension >1

11G20: Curves over finite and local fields

11G30: Curves of arbitrary genus over 

global fields

11F80: Galois Representations

11R23: Iwasawa theory

11R58: Arithmetic theory of algebraic function fields

11U05: Decidability: arithmetic problems

14G45: Perfectoid spaces

57K10: Knot theory