Research

I am very passionate about research in both Pure Mathematics (specifically Functional Analysis and Operator Algebras) and Undergraduate Mathematics Education.

Functional Analysis and Operator Algebras

• Currently, I am focused on proving Wigner-type theorems which stem from Wigner Theorem, an influential result in quantum mechanics.

Publications

• M. Allen, Solvability of (2k k) = (2a a)(x+2b b), (in review), arXiv preprint arXiv:2406.10404.

Undergraduate Mathematics Education

• I am focused on student understanding of common Calculus topics such as implicit differentiation and continuity.

• I am currently a research assistant for the 2024-2025 academic year with the NSF-funded STEM Gateway project, which aims to improve teaching in introductory STEM courses and boost retention rates.

Publications

• O. Buchbinder and M. Allen, Calculus I Students’ Understanding of Implicit Differentiation, Proceedings of the 25th Annual Conference on Research in Undergraduate Mathematics Education, 2024.

• O. Buchbinder, and M. Allen, Students’ Understanding of Implicit Differentiation, (journal article in preparation).