Emma O'Neil
Undergraduate Mathematics Student, Portland State University
I am a third-year mathematics student at Portland State University.
My main research interests are diagrammatic algebra, mathematical physics,
and quantum computation. I am currently working with the quantum information
science research group on on visualization of finite-dimensional quantum state spaces via toric
varieties, and on the structure of Cayley graphs of groups generated by certain sets of ternary quantum gates.
Outside of academics, I'm very interested in noise-based procedural terrain generation algorithms, and would
be happy to discuss this.
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Research
Quantum Information Science Research Group with Steven Bleiler and Marek Perkowski
Researching the use of toric varieties for visualization of state spaces of quantum systems for the purpose of quantum gate design, and Cayley graphs of groups generated by certain sets of ternary and higher-radix gates.
Ergodic Theory with J.J.P. Veerman
Ergodic theory of complete interval maps generalizing the Gauss map. Showed mixing of a class of expanding maps utilizing elementary methods and the transfer operator, without the classical functional analysis machinery.
MathILy-EST REU with Thomas C. Hull
Combinatorial geometry of origami, enumeration of locally flat-foldable states and properties of the reconfiguration graphs of the locally flat-foldable mountain-valley assignments on the Miura-ori.
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Publications
Visualizing the state space and transformations of higher order quantum logics via toric geometry.
Steven Bleiler, Shanyan Chen, Emma L. O'Neil, J. Eliot Reich, Julia Rezvani, Elijah Whitham-Powell, Ali Al-Bayaty, Jerzy Jegier, Sonia Yang, Marek Perkowski
Revised and resubmitted
Origami Flip Graph of the 2×n Miura-ori.
Lumi Christensen, Thomas C. Hull, Emma O'Neil, Valentina Pappano, Kacey Yang
Submitted, in revision.
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Talks
- Enumerating Valid Mountain-Valley Assignments on the Miura-ori Joint Mathematics Meetings, 2025
- Diameter of the 2×n Miura-ori Origami Flip Graph Joint Mathematics Meetings, 2025
- Ergodic Theory of Complete Interval Map Expansions Joint Mathematics Meetings, 2026
- Complete Interval Maps are Mixing (Slides link) PNW MAA Spring Sectional, 2026
- Complete Interval Maps are Mixing PiMUC, 2026 (upcoming)
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