About Me

In June 2020, I earned my Ph.D in mathematics at the University of Toronto. My supervisor was Prof. Kumar Murty and my co-advisor was Prof R. Sujatha. In Fall 2020, I was at CRM Montreal attending the Thematic Program on Cohomology in Arithmetic. Between January 2021 and December 2022, I was a PIMS Postdoctoral Fellow at UBC, Vancouver. I was affiliated with the Fields Institute between January and August 2023. Since Fall 2023, I am a tenure track assistant professor at UTRGV.

My curriculum vitae can be found here: CV.

I am currently recruiting Masters and PhD students for positions starting Spring/Fall 2025.

Research

My research interests include Diophantine equations, Iwasawa theory, and Beyond Endoscopy.

For my PhD thesis, I studied growth patterns of fine Selmer groups in infinite towers of number fields. I have also worked on questions in non-commutative Iwasawa theory.

Many questions which I study lie at the intersection of Iwasawa theory and arithmetic statistics. In particular, a long-term goal is to understand the average behaviour of the Iwasawa invariants for class groups and Selmer groups of elliptic curves. Questions pertaining to Iwasawa theory of graphs have also piqued my interest.

I think about questions related to Diophantine stability and Hilbert’s 10th Problem.

More recently, I have studied some questions related to the Iwasawa theory of graphs.

I am interested in Langlands’ Functoriality Conjecture and related problems in the Langlands program like the Langlands’ Beyond Endoscopy idea.

To know more about my research you can look at my research statement. If you prefer a shorter read, without much technical details you can look at this research statement.

Publications

1. On a conjecture of Mazur predicting the growth of Mordell-Weil ranks in \(\mathbb{Z}_p\)-extensions (with Rylan Gajek-Leonard, Jeffrey Hatley, and Antonio Lei)
   accepted (Math Research Letters)
   

2. Statistics for Anticyclotomic Iwasawa Invariants of Elliptic Curves (with Jeffrey Hatley and Anwesh Ray)
   Math Zeitschrift Volume 307, article number 49 (2024)
   Journal version

3. Studying Hilbert’s 10th Problem Via Explicit Elliptic Curves (with Antonio Lei and Florian Sprung)
   Math Annalen Volume 390, pages 5153–5183 (2024)
   Journal version

4. Statistics for Iwasawa Invariants of Elliptic Curves II (with Anwesh Ray)
   Int. J. Number Theory Vol. 20, No. 04, pp. 1099-1124 (2024)
   Journal version

5. \(\lambda\)-Invariant Stability in Families of Modular Galois Representations (with Jeffrey Hatley)
   Research in the Mathematical Sciences 10.3 (2023): article 33
   Journal version

6. Heuristics for anti-cyclotomic \(\mathbb{Z}_{p}\)-Extensions (with Lawrence Washington)
   Experimental Math Volume 33, 2024 - Issue 4
   Journal version

7. Cotorsion of Anti-Cyclotomic Selmer groups on average (with Florian Sprung)
   Proceedings of the American Math Society 152 (2024), 521-535
   Journal version

8. Rank Jumps and Growth of Shafarevich–Tate Groups for Elliptic Curves in \(\mathbb{Z}/p\mathbb{Z}\)-Extensions (with Lea Beneish and Anwesh Ray)
   J. Aus. Math. Society 116(1), 1-38 (February 2024)
   Journal version

9. Non-vanishing modulo \(p\) of Hecke \(L\)-values over imaginary quadratic fields (with Antonio Lei)
   Accepted for publication (Israel Journal of Mathematics)

10. Growth of \(p\)-parts of ideal class groups and fine Selmer groups in \(\mathbb{Z}_q\)-extensions with \(p\neq q\) (with Antonio Lei)
    Acta Arithmetica 207 (2023), 297-313
    Journal version

11. Structure of Fine Selmer Groups in abelian \(p\)-adic Lie extensions (with Filippo Nuccio and R. Sujatha)
    Osaka J. Math. 61(1): 121-146 (January 2024).
    Journal version

12. Control theorems for fine Selmer groups, and duality of fine Selmer groups attached to modular forms (with Jeffrey Hatley, Antonio Lei, and Jishnu Ray).
    The Ramanujan Journal 60 (2023), 237–258
    Journal version

13. Iwasawa Invariants for elliptic curves over \(\mathbb{Z}\)_\(p\) extensions and Kida’s Formula (with Anwesh Ray)
    Forum Math. 34 (2022), no. 4, 945–967
    Journal version

14. Arithmetic Statistics and Noncommutative Iwasawa Theory (with Antonio Lei and Anwesh Ray).
    Documenta Mathematica 27 (2022), 89-149.
    Journal version

15. Control Theorems for Fine Selmer Groups (with Meng Fai Lim).
    Journal de théorie des nombres de Bordeaux, 34 (2022) no. 3, 851-880.
    Journal version

16. Anticyclotomic \(\mu\)-Invariants of Residually Reducible Galois Representations (with Anwesh Ray).
    Journal of Number Theory 234 (2022): 476-498.
    Journal version

17. Statistics for Iwasawa Invariants of Elliptic Curves (with Anwesh Ray).
    Trans. Amer. Math. Soc. 374 (2021), no. 11, 7945–7965.
    Journal version

18. Analogue of Kida’s Formula for Fine Selmer Groups.
    Journal of Number Theory 222 (2021): 249-261.
    Journal version.

19. Perfect Powers that are Sums of Squares of an Arithmetic Progression (with Vandita Patel).
    Rocky Mountain Journal of Mathematics 51 (2021), No. 3, 933-949.
    Journal version

20. Growth of (Fine) Selmer Groups in Uniform pro-\(p\) Extensions.
    Annales mathématiques du Québec 45 (2021), 347–362.
    Journal version

21. Growth of \(p\)-Fine Selmer Groups and \(p\)-Fine Shafarevich-Tate Group in \(\mathbb{Z}/p\mathbb{Z}\) Extensions.
    Journal of the Ramanujan Math Society 36 (2021), No. 1.
    Journal version

22. Growth of Fine Selmer Groups in Infinite Towers.
    Canadian Mathematics Bulletin 63 (2020), Issue 4, 921-936.
    Journal version.

(For preprints you may check arXiv or my CV.)

Teaching

Spring 2025: MATH 4364 (Modern Algebra II)
Fall 2024: MATH 2318 (Linear Algebra)
Spring 2024: MATH 3363 (Modern Algebra I)
Fall 2023: MATH 2413 (Calculus I)

Previously, I taught Calculus (single and multi-variable) and first year Linear Algebra at the University of Toronto and UBC (Vancouver). While I was a graduate student at the University of Toronto, I was a Teaching Assistant for several courses.

To know about my teaching philosophy you can read my teaching statement.

Service

I was a member of the UBC Math Department’s Equity, Diversity, and Inclusion Committee for the academic year 2021-22.

Graduate Mentorship

I have mentored the following students for their Masters project/ thesis.
May – Nov 2024: Ama Quansah (UTRGV), Tribonacci numbers as a product of two Lucas numbers presentation

Undergraduate Mentorship

I have mentored the following students for their Bachelors project/ thesis.
Aug 2021 – April 2023: Adithya Chakravarthy (University of Toronto), thesis on Iwasawa Theory
Jan – May 2022: Vitthal Yellambalse (BITS Goa), reading project on cyclotomic fields
May – July 2023: Shubhrojyoti Dhara (ISI Bangalore), reading project on elliptic curves
May – June 2023: Léonie Chipot (UOttawa), learning to write mathematical proofs
Sep – Dec 2023: Samyak Jha (IIT Bombay), \(p\)-adic \(L\)-functions
Sep – Dec 2023: Raul Marquez (UTRGV), elliptic curves and \(L\)-functions
May – July 2024: Nandini Parkhi (IISER Bhopal), reading project on \(p\)-adic numbers
May – July 2024: Aniruddha Mondal (IISER Mohali), reading project on \(p\)-adic numbers
Sep – Dec 2024: Raul Marquez (UTRGV), root systems
May 2024 – present: Alejandro Delgado (UTRGV), elliptic curves

Outreach

I was a mentor for the University of Toronto High School Mentorship Program.
Winter 2018: Anna Krokhine (graph theory and combinatorics)
Winter 2019: Maya Bozzo-Ray (Benford’s Law)
Winter 2020: Jennifer Wang (Group Theory and Elementary Number Theory)

I gave an invited talk on Möbius Functions at the Summer Math Academy for high school students. I would also volunteer to run the monthly STEM Workshop.

I believe in the axioms laid out by Federico Ardila-Mantilla.

1. Mathematical talent is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.
   

2. Everyone can have joyful, meaningful, and empowering mathematical experiences.
   

3. Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.
   

4. Every student deserves to be treated with dignity and respect.
   

5. (My addition) Mathematics will be better with you in it.

Organization

While I was a graduate student, I organized the weekly GANITA seminars. I still attend these seminars whenever I can. If you are a number theorist wandering in the Toronto region, eager to interact with others of your kind, you are welcome to participate. Or better yet, give a talk!

I co-organized a mini-course on Iwasawa Theory at the 2019 CMS Winter Meeting. Here is a PDF.

You can click here to access the homepage of the seminar series meant to prepare participants for the workshop on Higher Coleman Theory and its Applications which was held at the CRM (December 7-11, 2020).

Between September 2021 and December 2022, I was an organizer of the weekly UBC Number Theory Seminar.

I was a co-organizer for the Beyond Endoscopy Mini Conference in April 2023.

I was a project leader at the Rethinking Number Theory Workshop in June 2023. See our preprint here.

I am currently organizing the Algebra/Number Theory Seminar at UTRGV with my colleague Luigi Ferraro.

I (co)-organized a special session on ‘Additive Number Theory and Modular Forms’ with my colleague Brandt Kronholm at the AMS Fall Sectional Meeting in San Antonio (Sep 14-15, 2024).

I will be (co)-organizing a special session on ‘Arithmetic Aspects of Galois Representations’ with Antonio Lei at the CMS Winter Meeting in Vancouver, BC (Nov 29 - Dec 2, 2024).

I will be (co)-organizing the 37th Automorphic Forms Workshop to be held at the University of North Texas, Denton (Apr 30 - May 4, 2025). This is funded by the NSF grant DMS-2442586.

Expository Talks, Articles, and Course Notes

1. MSRI Summer School (2017): Automorphic Forms and the Langlands’ Program
2. Introduction to Iwasawa Theory (of Fine Selmer Groups)
3. How to write a competitive postdoc statement - a presentation for graduate students at CMS 2024 (Vancouver)

Travel Calendar