# Debanjana Kundu

...learning to turn coffee into theorems

Email dkundu[at]math[dot]ubc[dot]ca

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. Starting January 2021, I am a PIMS Postdoctoral Fellow at UBC, Vancouver.

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. In the process, I provided non-trivial evidence for Coates-Sujatha Conjecture A. I have also worked on questions in non-commutative Iwasawa theory and have provided evidence for Coates-Sujatha pseudo-nullity conjecture.

Recently, 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.

I am also 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 and Preprints

1. Iwasawa Invariants for elliptic curves over $$\mathbb{Z}$$$$p$$ extensions and Kida’s Formula (with Anwesh Ray)
Accepted for publication (Forum Mathematicum)

2. Control theorems for fine Selmer groups, and duality of fine Selmer groups attached to modular forms (with Jeffrey Hatley, Antonio Lei, and Jishnu Ray).
Accepted for publication (The Ramanujan Journal)
Journal version

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

4. Control Theorems for Fine Selmer Groups (with Meng Fai Lim).
Accepted for publication (Journal de Théorie des Nombres de Bordeaux)

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

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

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

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

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

10. 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 (2021) Volume 36, No. 1.
Journal version

11. Growth of Fine Selmer Groups in Infinite Towers.
Canadian Mathematics Bulletin (2020) Volume 63 / Issue 4 pp. 921-936.
Journal version.

## Teaching

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

I have mentored the following students for their Bachelors project/ thesis.
Aug 2021-present: Adithya Chakravarthy (University of Toronto), thesis on Iwasawa Theory
Jan 2022-present: Vitthal Yellambalse (BITS Goa), reading project on cyclotomic fields

## 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. Unfortunately, I can no longer attend these seminars regularly. If you are a number theorist wandering in the Toronto region, eager to interact with others of your kind online, 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).

For the academic year 2021-22, I am a co-organizer of the weekly UBC Number Theory Seminar.