Education (degrees and institutions):
PhD in mathematics, The University of Texas at Arlington, 2020
MS in Mathematics, The Florida State University, 2014
BS in Mathematics, Florida Agricultural & Mechanical University, 2012

Research Interests 
Nature is full of movement or transformations. Symmetries describe what’s unchanged after these
transformations. For example, while a circle looks the same after any rotation, squares need multiples of
90 degrees to return to their original position. So the rotational symmetries of a square and a circle are
not equivalent. More involved symmetries are found in the study of Sophus Lie’s (think “Lee”)
transformation groups and their historical connection to solving (differential) equations that model
physical phenomena. A “cheat code” to studying transformation groups (called Lie groups) is found in
the notion of a Lie algebra. Going further, there are symmetries that can account for differences in spin
found in particle physics. Now we’ve arrived at the idea of a Lie superalgebra. One thing I do is
determine, break down, and describe infinite-dimensional representations of Lie superalgebras. In other
words, I realize abstract objects as transformations of spaces—symmetries known in the world today
(geometry, machine learning, molecular structures) and symmetries in theoretical development of
mathematical physics (that may or may not be seen in our lifetimes).

I’m also involved in other areas of mathematical and educational research, including generalized parking
functions and analysis of the journeys and experiences of people whom the mathematical community
others, especially in view of race.

Selected Publications 
Dwight Williams II's articles on arXiv: https://arxiv.org/a/williams_d_5.html
See also ORCID: https://orcid.org/0000-0003-2611-2388.

1) arXiv: https://doi.org/10.48550/arXiv.2311.14055
Interval and ℓ-interval Rational Parking Functions
Tomás Aguilar-Fraga, Jennifer Elder, Rebecca E. Garcia, Kimberly P. Hadaway, Pamela E. Harris, Kimberly
J. Harry, Imhotep B. Hogan, Jakeyl Johnson, Jan Kretschmann, Kobe Lawson-Chavanu, J. Carlos Martínez
Mori, Casandra D. Monroe, Daniel Quiñonez, Dirk Tolson III, Dwight Anderson Williams II

2) arXiv: https://doi.org/10.48550/arXiv.2206.00541
The American Mathematical Monthly: https://doi.org/10.1080/00029890.2023.2206311
On Parking Functions and The Tower of Hanoi
Yasmin Aguillon, Dylan Alvarenga, Pamela E. Harris, Surya Kotapati, J. Carlos Martínez Mori, Casandra D.
Monroe, Zia Saylor, Camelle Tieu, Dwight Anderson Williams II

3) arXiv: https://doi.org/10.48550/arXiv.2203.08068
Journal of Geometry and Physics: https://doi.org/10.1016/j.geomphys.2023.10478
Ghost center and representations of the diagonal reduction algebra of osp(1|2)
Jonas T. Hartwig, Dwight Anderson Williams II

4) arXiv: https://doi.org/10.48550/arXiv.2106.04380
Theoretical and Mathematical Physics: https://doi.org/10.1134/S0040577922020015
Diagonal reduction algebra for osp(1|2)
Jonas T. Hartwig, Dwight Anderson Williams II
(Also available in Russian: https://doi.org/10.4213/tmf10138)

5) Dissertation: https://rc.library.uta.edu/uta-ir/handle/10106/29148
Bases of infinite-dimensional representations of orthosymplectic Lie superalgebras
Dwight Anderson Williams II