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HI! I'm a Mathematician by day and a pun-loving, music-making, tetris-playing, board game-developing, church-going girly-pop... also by day :D

Iris Shi — Research CV

Mathematician working with arithmetic geometry, singular learning theory, and zero-knowledge proof systems. PhD research in Artin–Schreier curves, published in Proceedings of the AMS. Proved a new lower bound resolving part of an open problem on the learning-theoretic geometry of neural networks, contributed to the MAIS open-problems repository. Also built Plonktris, a full-stack ZK application in Rust using plonky2 with recursive IVC proving.

shi.iris0505@gmail.com iris-garvy Download PDF Jacksonville, FL

Education

University of Florida — PhD in Mathematics
2021 – 2026
  • Thesis: Artin–Schreier Curves with Minimal a-number (advised by Jeremy Booher)
University of Florida — BS in Mathematics, Minor in Statistics
2017 – 2021

Publications & Manuscripts

An Infinite Family of Artin–Schreier Curves with Minimal a-number
2025
Iris Y. Shi, Proceedings of the AMS · arXiv:2411.11201
  • Constructed infinite families of curves over finite fields with extremal invariants, resolving an open existence question using computational and deformation-theoretic methods.
A Width Bound for Quadratic Network Modular Addition
2026
Iris Y. Shi, MAIS Open Problems repository
  • Proved Hmin(p) ≥ (3p−1)/2, a new lower bound on the minimal network width admitting an exact fit to modular addition, via a Fourier normal form and a bilinear-complexity (Alder–Strassen) contraction argument.
[Iwasawa Theory and T-adic Exponential Sums]
Expected 2026
with Jeremy Booher · Manuscript in preparation.
  • Developed computational methods connecting p-adic L-functions and exponential sums, identifying structural similarities between previously disconnected invariants.

Research Talks

A T-adic computation of the Cartier
Mar 2026
The 2026 Gainesville Number Theory Conference
Artin–Schreier curves and the Cartier–Manin Matrix
Mar 2026
UF Graduate Math Colloquium
Artin–Schreier Curves with Minimal a-number
Nov 2025
Bayou Arithmetic Research Days 6
Riemann's Existence Theorem and Complex Patching
Sept 2025
UF Algebra Seminar

Technical Experience

PhD research tooling
github repo
  • Developed a search algorithm in MAGMA to identify and categorize Artin–Schreier curves with extremal properties.
  • Built a lightweight visualization tool for analyzing the complexity of large and sparse Cartier–Manin matrices.
  • Benchmarked p-adic and T-adic approaches for Cartier operator construction, identifying shared computational bottlenecks and optimizing the naive implementation to near O(n log n) through algorithmic improvements.
plonktris: a SNARK Tetris prover
plonktris.com
  • Designed PLONK circuits in plonky2 (Rust) verifying Tetris solutions as 33K-constraint systems over the Goldilocks field, with a recursive prover (chunked IVC via cyclic recursion) proving arbitrarily long solutions in bounded memory.
  • Found and fixed a soundness bug where an out-of-range collision index let invalid piece placements verify.

Teaching & Honors

Calculus and Linear Algebra Graduate Teaching Assistant, University of Florida
2021 – 2026
Mathematics Graduate Teaching Award
May 2025
Graduate Teaching Excellence Award
Dec 2024
Certificate of Teaching Excellence Award
Dec 2022

Technical Skills

Languages: Rust, Python, R
Mathematics: p-adic methods, elliptic and Artin–Schreier curves over finite fields, singular learning theory
Cryptography: plonky2, circom, noir, zero-knowledge proof systems
Other: MAGMA (computational algebra system), SageMath