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