Peikai Qi

My current mathematical interests are algebraic geometry and number theory, more specifically, Iwasawa theory, modular forms, elliptic curves, Massey products.

Papers and Writtings

Research projects

  • An Analogue of Greenberg's Pseudo-null Conjecture for CM fields (Joint with Matt Stokes, draft, 2024)
  • On the Non p-Rationality and Iwasawa Invariants of Certain Real Quadratic Fields (Joint with Matt Stokes, submitted,2024)
  • Iwasawa lambda invariant and Massey product (Submitted, 2024)

    • Papers with undergraduate students

    1. Combinatorial and Analytical Properties of Higher-Order Recursive Polynomial Sequences(2023), (joint with Luke Bridges, Max Budnick, Zachary Martin, Janine Wang, and Aklilu Zeleke. Draft in progress.)
    2. Multivariate Fibonacci-like Polynomials and their Applications(2022) (joint with Sejin Park, Etienne Phillips, Zhan Zhan, and Ilir Ziba)
    3. Universally uniformly continuous metric spaces(2017) (joint with Katrina Gensterblum, and Willie Wong)

    Talks

    Here are some notes and slides of talks that I gave. Some are exposition and some are about my research.
    Format Tittle
    Handwritting Knots and Primes,graduate student colloquium at MSU, Feb 20 2024
    Handwritting Almost Purity Theorem, Number theory learning seminar at MSU, Feb 9 2024
    Beamer Video Iwasawa lambda invariant and Massey products,Fields institution, online, Nov 13 2023
    Beamer Iwasawa lambda invariant and Massey products,Binghamton University Graduate Combinatorics, Algebra, and Topology Conference, Nov 12th 2023
    handwriting Introduction to Brauer Manin obstruction, Student algebra seminar at MSU, Oct 6th 2023
    handwriting Modular Curves, Student number theory seminar at MSU, Sep 13rd 2023
    slides Iwasawa \lambda invariant and Massey products, Number Theory and Combinatorics in Duluth: A conference to honor Joe Gallian and 45 years of the Duluth REU , Duluth, July 31st-August 4th 2023.
    pdf \Lambda Modules, Student algebra seminar at MSU

    Notes

    Here are some notes I took or wrote. Most of them are exposition note or summary of some papers that I read.
    Format Tittle
    Handwritting Congruence Module