Academic record

Curriculum vitae

Jimmy Vineyard

Department of Mathematics · The Ohio State University
vineyard.23@osu.edu · jwvineyard.github.io
ORCID: 0009-0006-4968-0918

Education

PhD in Mathematics, in progress

The Ohio State University · Columbus, OH

Fall 2026 – Present

MA in Mathematics

University of Wisconsin–Madison · Madison, WI

Sep. 2025 – May 2026

BA in Mathematics, with Honors in the Major

University of Wisconsin–Madison · Madison, WI
Minor in Computer Sciences · GPA: 3.9/4.0

Sep. 2021 – May 2025

Research interests

Combinatorics and algebraic geometry.

Publications & preprints

Publications

  1. Jimmy Vineyard. Concrete billiard arrays of polynomial type and Leonard systems. Linear Algebra and its Applications 710 (2025), 296–309.
    doi:10.1016/j.laa.2025.02.006
  2. Amy L. Cochran and Jimmy Vineyard. The Dynamics of Mood in Bipolar Disorder: How Mathematical Models Help Phenotype Individuals, Forecast Mood, and Clarify Underlying Mechanisms. Current Psychiatry Reports 27 (2025), 687–696.
    doi:10.1007/s11920-025-01647-z
  3. Peizhe Li, Jimmy Vineyard, Seungyeon Oh, and Jack Maloney. Integrating Local Learning into the Two-Stage Markov Task to Separate Model-Based from Model-Free Learning. SIAM Undergraduate Research Online 18 (2025).
    Project advisors: Haley Colgate Kottler and Amy Cochran.
    doi:10.1137/24S1703392

Preprints

  1. Kevin Kauflin, Paul Terwilliger, Barnabás Valkó, Jimmy Vineyard, and Hanyi Wu. The Terwilliger algebra for the distance-regular graphs with valency three. Preprint (2026).
    arXiv:2606.05393

Academic experience

Graduate student mentor

Madison Experimental Mathematics Lab · UW–Madison

  • Mentored undergraduate research in algebraic graph theory under Paul Terwilliger.
  • Led discussions and short lectures, and guided students in developing research skills.
Fall 2025 & Spring 2026

Mathematics course grader

University of Wisconsin–Madison

  • Fall 2024: Math 540, Linear Algebra II; Math 623, Complex Analysis.
  • Spring 2025: Math 341, Linear Algebra; Math 475, Introduction to Combinatorics.
Sep. 2024 – May 2025

Mathematical writing assistant

University of Wisconsin–Madison · Amy Cochran

  • Contributed to an invited review on mathematical models for bipolar disorder in Current Psychiatry Reports.
  • Conducted a literature review, communicated mathematical ideas to a broader audience, and drafted and revised the paper.
Summer 2024 &
Spring 2025

Research & reading

Directed reading in Lie algebras

Supervisor: Paul Terwilliger

Covered the Math 747 syllabus and the first eight chapters of Roger Carter’s Lie Algebras of Finite and Affine Type.

May – Jul. 2025

Senior honors thesis

Supervisor: Paul Terwilliger

Research in algebraic combinatorics, resulting in a publication in Linear Algebra and its Applications.

Jan. – Aug. 2024

Machine Learning for Example Generation in Pure Math

Madison Experimental Mathematics Lab · Supervisor: Jordan Ellenberg

Undergraduate group research project.

Sep. 2023 – May 2024

UW–Madison Analysis REU

Supervisor: Sergey Denisov

Six-week NSF Research Experiences for Undergraduates program in complex analysis.

May – Jun. 2023

Task Design to Distinguish Model-Free and Model-Based Learning

Madison Experimental Mathematics Lab · Supervisor: Amy Cochran

Undergraduate group research project, resulting in a publication in SIAM Undergraduate Research Online.

Jan. – May 2023

Directed Reading Program participant

University of Wisconsin–Madison

Reading projects on combinatorics, cryptography, and graph neural networks.

Fall 2021, Fall 2022,
Spring 2023

Honors & awards

Honors in the Major: Mathematics

UW–Madison College of Letters & Science

2025

Dean’s List

University of Wisconsin–Madison

Fall and Spring semesters of 2021 – 2022, 2023 – 2024, and 2024 – 2025.

2021 – 2025

UW–Madison Pathway Grant

University of Wisconsin–Madison · Four-year scholarship

2021 – 2025

Meritorious Winner, Mathematical Contest in Modeling

Consortium for Mathematics and its Applications

Top 8% worldwide; top three of 160 U.S. teams for Problem C, “Data Insights.”

2023

Fund for Wisconsin Scholars Grant

Fund for Wisconsin Scholars · $20,000 scholarship

2021

Talks & presentations

Transformation Groups of Varieties on Finite Fields

Park City Mathematics Institute · 20-minute talk

Jul. 2024

A 3-dimensional generalization of Pascal’s triangle and its connection to Leonard pairs

UW–Madison Combinatorics Seminar · 40-minute talk

Apr. 2024

Graph Neural Networks

UW–Madison Math Club · 45-minute talk

Feb. 2024

Local Learning in the Two-Stage Task to Distinguish Model-Based and Model-Free Learning

Joint Mathematics Meetings · Poster presentation

Jan. 2024

Outreach & service

Directed Reading Program mentor

University of Wisconsin–Madison

Led a directed reading project on cluster algebras.

Spring 2026

Vice president, Math Club

University of Wisconsin–Madison

Club administration, board coordination, and event planning.

May 2024 – May 2025

Events coordinator, Math Club

University of Wisconsin–Madison

Organized faculty talks, outreach and social events, mathematics competitions, and undergraduate talk nights.

Apr. 2023 – May 2024

Programming

Languages: Python, Julia, Java.
Python libraries: NumPy, pandas, PyTorch, SymPy.