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
My dissertation focused on proving Wigner-type theorems which stem from Wigner Theorem, an influential result in quantum mechanics.
Publications
Allen, M. (2026). Solvability of (2k k) = (2a a)(x+2b b). Integers Electronic Journal of Combinatorial Number Theory, 26, A26. https://math.colgate.edu/~integers/aa26/aa26.pdf
Undergraduate Mathematics Education
I am focused on student understanding of common calculus topics such as implicit differentiation and continuity.
I am currently working on analyzing students' self-regulated learning (SRL) skills in Calculus I and Calculus II.
Publications
Allen, M. & Buchbinder, O. (2026). Can Self-Regulated Learning Practices Shift Without Intervention? An Exploratory Study of Calculus I and II Students. In S. Cook, B.P. Katz, & K. Melhuish (Eds.), Proceedings of the 28th Annual Conference on Research in Undergraduate Mathematics Education (pp. 368–377). SIGMAA on RUME. Alexandria, VA. http://sigmaa.maa.org/rume/RUME28(2026)_Proceedings.pdf
Buchbinder, O. & Allen, M. (2025). Calculus I Students’ (Logical) Reasoning about the Definition of Continuity of Function. In S. Cook, B.P. Katz, & K. Melhuish (Eds.), Proceedings of the 27th Annual Conference on Research in Undergraduate Mathematics Education (pp. 553–561). SIGMAA on RUME. Alexandria, VA. http://sigmaa.maa.org/rume/RUME27_Proceedings.pdf
Buchbinder, O. & Allen, M. (2024). Calculus I Students’ Understanding of Implicit Differentiation. In S. Cook., B., Katz., & D. Moore-Ruso (Eds)., Proceedings of the 26th Annual Conference on Research in Undergraduate Mathematics Education, (pp. 423-430), Omaha, NE. http://sigmaa.maa.org/rume/RUME26_Proceedings.pdf
Buchbinder, O. & Allen, M. Students’ Understanding of Implicit Differentiation, (in review)