PhD. in Pure Mathematics
Sept. 2023 - Present
University of East Anglia
Norwich, Norfolk, United Kingdom
Dissertation Title: "Large Cardinals without the Axiom of Choice"
M.S. in Mathematics
Sept. 2019 - May 2021
Ohio University
Athens, Ohio, Unites States
B.A. in Mathematics
Sept. 2016 - May 2019
University of Northern Iowa
Cedar Falls, Iowa, United States
Associate Tutor
University of East Anglia, Norwich, Norfolk, United Kingdom
Sept. 2023 - Present
Courses Taught:
Mathematics for Scientists A - Algebra Skills, Exponentials and Logarithms, Trigonometry, Geometry, Calculus
Mathematics for Computer Science - Linear Algebra, Calculus, Sequences and Series, Differential Equations
Computation and Modelling - Linear Algebra, Python Programing, Data Processing, Data Visualization, Differential Equations
Mathematics for Scientists B - Python Programing, Data Processing, Data Visualization, Numerical Methods for Calculus and Differential Equations
Proofs and Limits - Proof Writing, Number Theory, Real Analysis
Probability and Multivariable Calculus - Probability Theory, Combinatorics, Multivariable Calculus
Complex Functions - Complex Numbers, Holomorphic Functions, Topology, Complex Analysis
Adjunct Lecturer
William Penn University, Oskaloosa, Iowa, United States
May 2022 - Present
Course Taught:
College Algebra - Algebra Skills,
Advanced Functions - Exponentials and Logarithms, Trigonometry
Independent Tutor
Self-Employed
2019 - Present
Topics Tutored:
Secondary School Mathematics - Algebra Skills, Exponentials and Logarithms, Trigonometry, Geometry
Computer Science: Python Programing, Data Science
Linear Algebra: Linear Algebra, Vector Spaces
Analysis: Calculus, Multivariable Calculus, Real Analysis, Measure Theory, Topology
Statistics - Actuarial Mathematics, Statistics, Multi Probability Theory
Combinatorics
Graph Theory
Proof Writing
Lecturer, Ellsworth Community College
Ellsworth Community College, Iowa Falls, Iowa, United States
May 2021 - May 2022
Courses Taught:
College Algebra - Algebra Skills, Geometry
Advanced Function - Exponentials and Logarithms, Trigonometry
Statistics - Statistics, Linear Regression, Probability Theory, Combinatorics
Teaching Assistant, Ohio University
Ohio University, Athens, Ohio, United States
Sept. 2019 - May 2022
Courses Taught:
College Algebra - Algebra Skills, Geometry
Advanced Function - Exponentials and Logarithms, Trigonometry
Current Research Projects
Large Cardinals Without the Axiom of Choice
Forcing with Reinhardt Cardinals
Contributed Talks
Sets and Models Seminar, University of Leeds
February 2025
Title: Large Cardinal Axioms near Kunen's Inconsistency
Abstract: In 2024 Farmer Schlutzenberg published a phenomenal result. In ZF set theory without the Axiom of Choice, the existence of an I0-embedding is equiconsistent with the existence of a non-trivial elementary embedding from $V_{\lambda + 2}$ into itself where $\lambda$ is the supremum of the critical sequence. Here we summarize a few key parts of this proof and give a few negative results on some related conjectures.
Set Theory in the United Kingdom, University of Cambridge
November 2024
Title: Periodicity and Kunen's Inconsistency
Abstract: In 2021, Gabriel Goldberg and Farmer Schlutzenberg showed there is a fundamental difference between the structure of the cumulative hierarchy at even and odd levels. This led to new result by Schlutzenberg to show that without the Axiom of Choice (AC) an I0-embedding, one of the strongest large cardinal axioms not known to be inconsistent with AC, is equiconsistent with a Kunen embeddings, one of the weakest large cardinal axioms known to be inconsistent AC. In this talk I introduce a few realted conjectures of mine following a similar path that in ZF there are more equiconsitencies between large cardinal axioms not known to be inconsistent with the AC and large cardinal axioms known to be inconsistent with the AC and some prelimanary results I have obtained.
120 Years without Choice Conference, University of Leeds
8-12 July 2024
Poster: Large Cardinal Axioms near Kunen's Inconsistency
Abstract: Summarizing new results by Gabriel Goldberg and Farmer Schlutzenberg, along with my own related conjecture and some preliminary results on it.
Conference and Seminar Organization
Logic Reading Group
Algebra, Number Theory, Logic, and Representations Research Group - University of East Anglia
2024 - Present
Topics: Set Theory, Type Theory
Big Talk Seminar
School of Engineering, Mathematics, and Physics, University of East Anglia
2025 - Present
Big Day Conference
School of Engineering of Mathematics, and Physics, University of East Anglia
12 June 2025
Joint LYMODS-SEEMODS Meeting
University of East Anglia
4-5 June 2025
SEEMOD Annual Meeting
University of East Anglia
March 2024
Research Organizations
European Set Theory Society
Set Theory in the United Kingdom
American Mathematical Society
London Mathematical Society
Southeast and Eastern Model Theory Network
Algebra, Number Theory, Logic, and Representations Research Group - University of East Anglia
Outreach Events
MathsJam
2023-2025
MathsJam is a international group of free events focused on finding and creating a sense of community of adults from all backgrounds who are interested in mathematics and puzzles. Evey month a new set of puzzles are created and shared around the world. Local volunteers create meetups in their areas to foster this community.
I came across this event while earning my PhD at the University of East Anglia. I became a regular attendee and volunteered to help organize our local meetings.
University of East Anglia, Great Yarmouth Science Days
Spring 2025
A science focused outreach event hosted by University of East Anglia to engage children between the ages of 12-14 with interesting science experiments. The goal is to show young students in rural areas what pursuing a higher education is about and what kind of problems you learn to solve!
In the mathematics section of these days we brought students through a 3 part workshop/demonstration of interesting fluid dynamics. We showed students examples of High Viscous Flows (Stoke's machines), Ferrofluid, and, the overall favorite of most students, non-Nuetonian Fluids (oobleck). We talked to students about the fundamental equations of fluid dynamics and how if one variable gets very big or small, it explains the experiments they are seeing in front of them.
General Audience Mathematics Talks
Existential Questions and Mathematical Crises
Big Day Conference - School of Engineering of Mathematics, and Physics, University of East Anglia
Summer 2025
Abstract: Questions about the existence of mathematical objects with specific properties are a common site across all of mathematics and science in general. in this talk we examine how a simple existential question "What is the exact size of the Real Numbers" gave rise to nearly a century long crises, leading to the formalization of mathematics, the creation of Set Theory, and a novel new proof technique.
Mathematics of Finite and Infinite Games
Big Talk Seminar - School of Engineering, Mathematics, and Physics, University of East Anglia, Norwich, Norfolk, United Kingdom
Spring 2025
Abstract: Games, both real and abstract, form a natural basis for describing many mathematical problems. In this talk we examine common questions that arise when talking about games. Issues such as complexity, solvability, and more. We end by comparing many well known games from around the world on these metrics.
Electoral College Explained
American Memorial Library, Norwich, Norfolk, United Kingdom
Fall 2024
Abstract: With the 2024 US Presidential Elections on the way we see many news headlines talking about the Electoral College. But how exactly does it work? and why does it work this way? In this talk we go through early history of the United States and how this history led to the Electoral College we see today. We discuss the mathematics of how the number of votes a state has is decided and make our own example using the same system but in the context of the counties of East Anglia.
Introduction to Voting Theory
Big Talk Seminar - School of Engineering, Mathematics, and Physics, University of East Anglia, Norwich, Norfolk, United Kingdom
Summer 2024
Abstract: Voting Theory is a branch of mathematics focused on understanding the nuances of relational systems. In this talk we define the abstract notion of voting system, showing how the United States Electoral College and Israeli Knesset fit into this definition. We then go to naively attempt to define rules of "fairness" for a voting system. For each rule we find a smallest example where this rule is violated. We end the talk with a discussion of Arrow's Incompleteness Theorem.
American Memorial Library, American Scholar 2023-2026
American Memorial Library, Memorial to the 2nd Air Division, 8th Air Force, United States Army Air Forces, Norwich, Norfolk, United Kingdom
The American Memorial Library (AML) is the only memorial library in the United Kingdom! The AML is a living memorial established after the end of World War II, in dedication to the American men and women who came to East Anglia to fly dangerous day-time missions, fight in the D-Day invasion, and support missions over the entirety of the European Theater. After the war the AML was created to serve as a living connection between the people of East Anglia, the American servicemen, and all their families.
I am honored to be the three time recipient of the American Scholar award from the AML, while completing my PhD. at the University of East Anglia. As a part of my time at the University of East Anglia, I worked at the AML to support the memorials mission, by being the connection between the American people and the people of East Anglia. One of my favorite parts of this work was helping people research their family history, connecting the British people whose relatives were from the 2nd Air Division, with their extended families in the United States. Along side this, I helped organize and implement a variety of events for the AML, to showcase American culture and learn about American history and government. I even gave a talk on history and mathematics of the Electoral College leading up to the 2024 Presidential Elections!
University of East Anglia, Post-Graduate Researcher Representative
University of East Anglia, Norwich, Norfolk, United Kingdom
Representing people has always been important to me. While completing my PhD. at the University of East Anglia, I took on the responsibility of representing my fellow Post-Graduate Researchers (PGRs) to the University administration. In this position I would bring forward any issues that were affecting PGRs to the heads of the School of Engineering, Mathematics, and Physics and the Graduate College. I would also help plan an organize events for on campus for PGR's from both my School and the entire Faculty of Science. These including organizing the Big Day PGR conference and a Christmas Dinner for the School of Engineering, Mathematics, and Physics and helping organize a BBQ for the Faculty of Science.
For a pdf version of my CV please contact me by email.