Since the beginning of the year, five papers co-authored by Assistant Professor of Mathematics Jose Ceniceros have been published.
Early this year, “Polynomial invariants of singular knots and links” appeared in the Journal of Knot Theory and Its Ramifications. Ceniceros, along with Indu Churchill of SUNY Oswego and Mohamed Elhamdadi of the University of South Florida (USF), presented research in which they “generalized the notion of the quandle polynomial to the case of singquandles,” proving that “the singquandle polynomial is an invariant of finite singquandles.”
“Legendrian rack invariants of Legendrian knots” was published online in March and in the July print issue of Communications of the Korean Mathematical Society. In this article, Ceniceros and his co-authors, USF’s Elhamdadi and Sam Nelson of Claremont McKenna College, “define a new algebraic structure called Legendrian racks or racks with Legendrian structure, motivated by the front-projection Reidemeister moves for Legendrian knots.”
In April, “Cocycle Enhancements of Psyquandle Counting Invariants” was published in the International Journal of Mathematics. Nelson co-authored the article in which “enhancements of the psyquandle counting invariant via pairs of a biquandle 2-cocycle and a new function satisfying some conditions” are defined.
Two papers, co-authored with Elhamdadi and Alireza Mashaghi of Leiden University in the Netherlands, have also been published. These papers are part of a new branch of Ceniceros’ research that uses knot theory to model and classify folded linear chains that appear in biology.
“Coloring Invariant for Topological Circuits in Folded Linear Chains” was published in Symmetry in May, as part of a special issue on “Topological Methods in Chemistry and Molecular Biology.”
Ceniceros and his fellow researchers adapted and applied “the algebraic structure of quandles to classify and distinguish chain topologies within the framework of circuit topology,” a mathematical way to categorize the arrangement of contacts within a folded linear biomolecular chain, such as those found in protein molecules or the genome.
They studied basic circuit topology motifs and defined quandle coloring for them, then explored “the implications of circuit topology operations that enable building complex topologies from basic motifs for the quandle coloring approach.”
Last month, “Enhancement of the coloring invariant for folded molecular chains” was published in the Journal of Mathematical Physics. In this article, the authors “considered a modified theory of singular knots that models folded linear molecular chains.” They enhanced the resolving power of the quandle coloring approach and demonstrated that “enhanced coloring invariants can distinguish fold topologies with an improved resolution.”