Hi there 👋

Gaurish Korpal here!

I often have directed reading project (DRP) ideas in number theory suitable for motivated undergraduates. Please email me to learn more about potential (online/in-person) projects.

During a DRP, you'll study a topic in number theory for two to three months and have weekly discussions with me. At the end of the reading period, you'll write a short report and present your readings at either your institute (in person) or the DRP symposium (online via Zoom).

• Fall 2024 (August 2024 to December 2024)
  • Aadi Kanwar - University of British Columbia, Canada (BS, 2027)
    • Investigating Variations in Ulam Spirals
• Spring 2024 (January 2024 to May 2024)
  • Achuthkrishnan Manoj - St. Stephen's College, University of Delhi, India (BSc, 2024)
    • Riemann Hypothesis
  • Muyuan Li - University of Arizona, USA (BS, 2027)
    • Permutation Puzzles
• Fall 2023 (July 2023 to December 2023)
  • Süeda Şentürk Avcı - Boğaziçi Üniversitesi, Türkiye (BS, 2024)
    • Dirichlet Class Number Formula for Imaginary Quadratic Fields
  • William Sean Hendarto Wihardja - Institut Teknologi Bandung, Indonesia (BS, 2024)
    • Higher Reciprocity Laws
  • Mochammad Zulfikar Aditya - Institut Teknologi Bandung, Indonesia (MS, 2020)
    • Quadratic Number Fields
  • Hun Sivmeng - Royal University of Phnom Penh, Cambodia (BS, 2024)
    • Binary Quadratic Forms

1. Get an opportunity to explore topics in number theory! Also check out Polymath Jr., Twoples, and DRP Türkiye.
2. Learn about tools like LaTeX, Sage, and Git that can help one become a better researcher. To know more about their importance, connect with code4math.

1. I just love to discuss number theory with people.
2. It will also allow me to finally read that book/paper I never had time for!

As an undergraduate, I did eight DRPs (elementary01, elementary02, elementary03, algebraic01, algebraic02, analytic01, analytic02, geometric01) with various professors in India. The following is my favorite:

• Title: Number Fields (algebraic01)
• Summary: I spent two months learning about algebraic number theory with Prof. Ramesh Sreekantan (ISI Bangalore). The main reference was Marcus' textbook "Number Fields" which is a standard introductory textbook on algebraic number theory where a big part of the theory is built via exercises. Therefore, I solved many exercises from this book. However, along the way, I also did some explorations using SageMath.
• Report: https://gkorpal.github.io/technical/2016-07-31-number-fields
• I later presented what I learned in a student seminar at my institute (NISER Bhubaneswar): https://gkorpal.github.io/lecture/2016-08-20-germain

1. You tell me which aspect of number theory you would like to explore (elementary, algebraic, analytic, topological, geometric). This mainly depends on your background and interests. If you are not sure, then I can help you choose.
2. I assign you a primary (and secondary) reference based on your mathematical maturity level (e.g. won't ask you to read Marcus' textbook without knowing Galois theory)
3. You make a reading plan (how many hours per week to spend on this and when to start/finish).
4. We meet regularly to discuss what you learned and, if needed, make adjustments to the plan.