Assistant Professor of Mathematics Jose Ceniceros co-authored an article published recently in the Mediterranean Journal of Mathematics.
In “Cocycle Invariants and Oriented Singular Knots,” Ceniceros and his co-authors discussed research in which they “extend the quandle cocycle invariant to oriented singular knots and links using algebraic structures called oriented singquandles and assigning weight functions at both regular and singular crossings.”
They said the resulting “invariant coincides with the classical cocycle invariant for classical knots, but provides extra information about singular knots and links. The new invariant distinguishes the singular granny knot from the singular square knot.”
Ceniceros was also invited to submit a video presentation on his current knot theory research to CVCK*, an asynchronous seminar on knot theory by The Ohio State University.
In a presentation titled “Cocycle Enhancements of Psyquandle Counting Invariants,” Ceniceros discusses psyquandles and their application to oriented pseudoknots and oriented singular knots.