Broadly, my research is in algebraic combinatorics. This can take many forms, across my work at Wisconsin with my advisor and a burgeoning array of collaborative projects.
Undergraduate Research:
This is my publication from my 2016 Math REU at UT Tyler: 2018 Paper On Uniformly Most Reliable Two-Terminal Graphs w/ C. Graves, M. Sun, H. Bertrand.
Graduate Research:
Math 741 Final Paper (Fall 2018; modifications made in 2019): Math 741 Final Paper: A New And Improved Snazzy Way to analyze SL2(Z)
Math 863 Final Paper (Spring 2020): Stable Gonalities and Sanity Checks
Specialty Exam Talk (February 21, 2022): The q-Onsager Algebra and the Quantum Plane
Paper completed April 2023: The q-Onsager Algebra and the Quantum Torus: https://arxiv.org/abs/2304.09326, J. Combin. Theory Ser. A 208 (2024), Paper No. 105939.
Paper in collaboration with several others, completed May 2024: The e-positivity of the chromatic symmetric function for twinned paths and cycles: https://arxiv.org/abs/2405.17649. Discrete Math. 348 (2025), no. 12, Paper No. 114687.
Paper in collaboration with several others, completed November 2024: Promotion, Tangled Labelings, and Sorting Generating Functions: https://arxiv.org/abs/2411.12034.
Paper in collaboration with several others, completed December 2024: The support of Kostant's weight multiplicity formula is an order ideal in the weak Bruhat order: https://arxiv.org/abs/2412.16820.
Paper completed April 2025: Using the quantum torus to investigate the q-Onsager algebra: https://arxiv.org/abs/2504.13362.
Thesis Defense Talk (June 2, 2025): The q-Onsager Algebra and the Quantum Torus
Outreach and Mentoring:
In Spring 2019 and Spring 2023, I served as a graduate student mentor for the UW-Madison Mathematics Department's Directed Reading Program.
In Fall 2023, I served as a graduate student mentor for the Madison Experimental Mathematics Lab, guiding four undergraduates in a research project.
In 2023, 2024, and 2025, I served as a problem writer and grader for the Mega Math Meet, a competition for local 5th and 6th grade students.
Contact: email is preferred (ogoff at wisc.edu)