Connor Meredith
Office: Previously Math 328
Email: connor.meredith0913@gmail.com
Office: Previously Math 328
Email: connor.meredith0913@gmail.com
About Me I am a CU Boulder alumnus and received my Ph.D. in Mathematics in May 2024. My dissertation is titled Nilpotence and Dualizability of Algebras of Finite Type. Feel free to send me an email and I will send you a copy. I am currently adapting my dissertation to submit for publication.
Advisor: Keith Kearnes
Research Interests: Universal Algebra generally. Natural Dualities and Tame Congruence Theory specifically.
Papers
Nilpotence and Dualizability of Algebras of Finite Type: 2024 Ph.D. Dissertation. This paper proves that all nilpotent, nonabelian, constantive expansions of cyclic groups of semiprime order are nondualizable. It also proves that localization of an algebra by an idempotent unary term operation preserves dualizability. I use this result to construct an algebra that settles a previously open question about the relationship between dualizability and nilpotence. Finally, I prove that in Mal'cev algebras, higher commutators in localizations are closely controlled by higher commutators in subalgebras.
Neutrabelian Algebras and the Split Centralizer Condition: 2019 Master's Thesis. This paper examines the dualizability of finite algebras belonging to congruence modular varieties. We prove that, under certain assumptions, the congruence lattice of an algebra satisfies a strong form of the split centralizer condition if and only if all of its subdirectly irreducible subalgebras are neutrabelian. An adaptation of this thesis was published in Algebra Universalis in 2021, authored by me, Keith Kearnes, and Ágnes Szendrei: Springer Link, arXiv Link.