UBC is located on the traditional, ancestral, and unceded territory of the xʷməθkʷəy̓əm (Musqueam) First Nation.

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; 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

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 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 version, Link 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 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.

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