Research & Study

My present and past studies and research plan and theme

Mutiple Zeta Values:

\[\zeta(k_1,k_2,k_3,\cdots k_r)=\sum_{m_1>m_2>m_3>\cdots m_r>0} \frac{1}{m_1^{k_1}m_2^{k_2}m_3^{k_3}\cdots m_r^{k_r}} \text{ } \forall k_1 \geq 2,k_i \geq 1,i \neq 1\]

Past and present field of study（これまでの専攻分野）

I have completed my MSc. from the Indian Institute of Technology (IIT), Delhi, India in 2024. Previously, I was a Bachelor student at Ramakrishna Mission Vidyamandira, Belur Math, Howrah, West Bengal, India.

MSc: During MSc, I had several courses such as Group Theory, Ring Theory, Field Theory, Linear Algebra, Complex Analysis, Functional Analysis, Topology, Measure Theory, C programming, Numerical Analysis, Probability. Besides semester courses, I took Algebraic Topology, Number Theory, and Commutative Algebra as additional courses. I also did a summer project on “Algebraic Topology” and an MSc reading project on “Morse Theory” and “3D Manifold”, all under the supervision of Dr. Biplab Basak, IITD.

BSc: During my three years of BSc, I have had courses in Real Analysis (4 semesters), Metric spaces (1 semester), Group theory (2 semesters), Linear algebra (4 semesters), Rings and Field theory (2 semesters), Topology, Measure theory, Complex Analysis, Numerical Analysis (1 semester), Ordinary and Partial Differential Equations (2 semesters), Particle dynamics and Analytical Statics, Analytical geometry of 2 and 3 dimensions (1 semester). I also had courses in Statistics and Computer Science as minor subjects. My BSc thesis was on “$\mathcal{L}^p$ Spaces”, advisor – Dr. Arnab Jyoti Dasgupta, Ramakrishna Mission Vidyamandira, Belur Math. In 2022, I appeared for the TIFR Bangalore written examination for MSc admission and cracked it, and also appeared for the Joint Admission Test for Masters (JAM) and secured 82 all-India rank (AIR), the highest rank in the mathematics department of my BSc college.

Self-Study & Exploration

  1. Galois theory: I read the basics of Galois Theory from Galois Theory [Tom Leinster, University of Edinburgh]
  2. Algebraic topology: I had an extra course in IIT Delhi on Algebraic topology, and I read it from Algebraic Topology by Alen Hatcher
  3. Knot theory: I read a bit of Knot Theory from resources like The Knot Book and YouTube lectures.
  4. Algebraic Number Theory: I studied it from A Text Book of Algebraic Number Theory.
  5. Commutative Algebra: From YouTube lecture
  6. I learned python, c,kotlin jetpack compose, andorid development, web development. I created a clone of whatsapp, “myChattingApp”

Past Projects

  1. BSc Project – $\mathcal{L}^p$ Spaces
  2. MSc Project – Morse Theory on 3D Manifolds

Research theme（研究テーマ）

Since my area of interest lies in Analysis, Algebra, and Number Theory related fields, my research theme will be Analytical Number Theory, Algebraic Number Theory, and these related fields, where combined ideas of analysis, and number theory, algebra are needed. After a very long research about works of Japanese mathematicians, and discussions with my professors, I came to know that Japan is the best place for doing the topics and related fields I am interested in, after the type of course work I have done in my undergraduate years. I am particularly interested in “Multiple Zeta Values” as analytical number theory. After going through the coursework and talks of Professor Henrik Bachmann from the Graduate School of Mathematics of Nagoya University, I understood that he can best guide me in this regard. In my Master’s days, I took advice from Prof. Viswanathan Puthan Veedu, who has also done numerous works on Topology, Complex Analysis, and Number Theory, and he also suggested me Japan would be best for me according to my interest in new problems and research topics. I believe I can do my best research work in my PhD in Japan.