Irish Debbarma bio photo

Irish Debbarma

Masters in Mathematics at Indian Institute of Science, Bangalore

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I am Irish Debbarma, a masters student at the Indian Institute of Science, Bangalore. I am majoring in mathematics from the Mathematics Department. I am from the state of Tripura in the North-Eastern part of India. You can find my CV here

Besides math, I am also interested in reading about history, geopolitics and linguistics.

I am a regular football player with loyalties to no club. I enjoy cycling and travelling as well.

Research Interests

Although I am fairly interested in anything in number theory, the following topics interest me a lot and I would like to read more about them.

  • Modular forms, congruences between modular forms.
  • Galois representations.
  • Automorphic representations.

Projects (Past and Current)

  • Currently, I am reading Coates-Wiles theorem from Coates-Wiles original paper.
  • For my Master’s thesis, I read the Gross-Stark conjecture. In particular the work of Dasgupta-Darmon-Pollack and Dasgupta-Kakde-Ventullo. This project is being supervised by Prof. Mahesh Kakde at IISc Bangalore. A draft thesis can be found here, and the final thesis here
  • My Bachelor thesis (submitted at the end of Spring 2023) was on Tate’s thesis Fourier Analysis in Number Fields and Hecke’s Zeta Functions under the guidance of Prof. Mahesh Kakde at IISc Bangalore. Please find a my thesis here
  • In the spring semester 2023, we read Linear Algebraic Groups from T.A. Springer’s Linear Algebraic Groups with an aim to understand reductive groups. This was done under the guidance of Prof. Shaunak Deo.
  • I studied $p$-adic $L$-functions from Introduction to Cyclotomic Fields by Lawrence Washington independently.
  • I studied The Uncertainty Principle in finite abelian groups with an aim to apply it to certain additive problems and extend it later to non abelian framework. I did this project under the guidance of Prof. Gautami Bhowmik of University of Lille, France. I was supported financially by Charpak Lab scholarship and GARP funding by IISc, Bangalore. You can find my report here
  • In the winter of 2021, I went through the proofs of Cubic and Biquadratic reciprocity laws from the book Introduction to Modern Number Theory by Ireland and Rosen under the guidance of Prof. Shaunak Deo.
  • I read about Zero-sum problems in Finite Abelian Groups under the supervision of Prof. Venkatesh Rajendran of maths Department, IISc . Work started from June mid and should continue till August mid formally but most likely continue for the whole year. I am trying to understand the structure of Finite Abelian Groups and find the value of related constants such as the Davenport’s constant, Erdös-Ginzberg-Ziv constant, Olson constant. The problem is still open and has very nice connections to other problems especially Non-unique factorisations in finite fields. Please find an incomplete report here
  • In the summer of 2020, I did a reading project under Prof. B. Sury of Indian Statistical Institute, Bangalore . It was on the topic of Binary Quadratic Forms . I had solved Niven chapter 1-3 and then wrote a report on Binary Quadratic Forms, their reduction and also tried understanding Zagier’s proof of Primes of the form 4k+1 as sum of two squares with the help of Binary Quadratic forms, and also read a bit about Gauss class problem. (report )

Presentations and miscellaneous notes

  • Finiteness of Integral points on elliptic curves click here
  • Kubota-Leopoldt’s $p$-adic $L$-functions click here
  • Tate’s thesis (Bachelor thesis presentation) click here
  • Prime Time seminar talk on Weil’s 1949 paper “Number of solutions of equations in finite fields” announcing the Weil conjectures. Please find the notes for this talk here. To be updated soon.
  • Hecke theory for automorphic representations in $GL_{1}$. Notes to be added soon.
  • Exposition on Serre’s conjecture on $2$ dimensional Galois representations. Notes to be added soon.
  • IISc Open Day 2023 poster, click here
  • IISc Open Day 2024 poster, click here

Contact Information

  • Personal email : irishdb29 [at] gmail [dot] com
  • Work email : irishd [at] iisc [dot] ac [dot] in
  • Twitter : @bourbakirish
  • LinkedIn : Irish
  • Address: N-Block hostel, Room number : 222