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.

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.

I have started studying questions which 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.

More recently, I have started thinking about questions related to Diophantine stability and Hilbert’s 10th Problem.

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

Studying Hilbert’s 10th Problem Via Explicit Elliptic Curves (with Antonio Lei and Florian Sprung)
Accepted for publication (Math Annalen)
Statistics for Iwasawa Invariants of Elliptic Curves II (with Anwesh Ray)
Accepted for publication (International Journal of Number Theory)
\(\lambda\)-Invariant Stability in Families of Modular Galois Representations (with Jeffrey Hatley)
Accepted for publication (Research in Mathematical Sciences)
Journal version
Heuristics for anti-cyclotomic \(\mathbb{Z}_{p}\)-Extensions (with Lawrence Washington)
Accepted for publication (Experimental Math)
Journal version
Cotorsion of Anti-Cyclotomic Selmer groups on average (with Florian Sprung)
Accepted for publication (Proceedings of the AMS)
Journal version
Rank Jumps and Growth of Shafarevich–Tate Groups for Elliptic Curves in \(\mathbb{Z}/p\mathbb{Z}\)-Extensions (with Lea Beneish and Anwesh Ray)
Accepted for publication (Journal of the Australian Mathematical Society)
Journal version
Non-vanishing modulo \(p\) of Hecke \(L\)-values over imaginary quadratic fields (with Antonio Lei)
Accepted for publication (Israel Journal of Mathematics)
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
Structure of Fine Selmer Groups in abelian \(p\)-adic Lie extensions (with Filippo Nuccio and R. Sujatha)
Accepted for publication (Osaka Journal of Mathematics)
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
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
Arithmetic Statistics and Noncommutative Iwasawa Theory (with Antonio Lei and Anwesh Ray).
Documenta Mathematica 27 (2022), 89-149.
Journal version
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
Anticyclotomic \(\mu\)-Invariants of Residually Reducible Galois Representations (with Anwesh Ray).
Journal of Number Theory 234 (2022): 476-498.
Journal version
Statistics for Iwasawa Invariants of Elliptic Curves (with Anwesh Ray).
Trans. Amer. Math. Soc. 374 (2021), no. 11, 7945–7965.
Journal version
Analogue of Kida’s Formula for Fine Selmer Groups.
Journal of Number Theory 222 (2021): 249-261.
Journal version.
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
Growth of (Fine) Selmer Groups in Uniform pro-\(p\) Extensions.
Annales mathématiques du Québec 45 (2021), 347–362.
Journal version
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
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

In Spring 2024, I am teaching MATH 3363 (Modern Algebra I).

In Fall 2023, I taught MATH 2413 (Calculus I).

I have 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 have also been 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.

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 (CMI), 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 2023 – present: Raul Marquez (UTRGV), \(L\)-functions

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.

Mathematical talent is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.
Everyone can have joyful, meaningful, and empowering mathematical experiences.
Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.
Every student deserves to be treated with dignity and respect.
(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.

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

I will be organizing a special session with my colleague Brandt Kronholm at the AMS Fall Sectional Meeting in San Antonio (Sep 15-16, 2024).

Debanjana Kundu