Jose Ceniceros
In the past two years, Assistant Professor of Mathematics Jose Ceniceros has worked with several knot theory researchers to explore and develop the theory of singular knots.

Ceniceros and fellow researchers Indu R. Churchill of SUNY Oswego, Mohamed Elhamdadi of the University of South Florida, and Mustafa Hajij of Santa Clara University, have now published an article that collects several of their recent results involving invariants defined using two different algebraic structures.

Singquandles, psyquandles, and singular knots: A survey” appears online in the Journal of Knot Theory and Its Ramifications. The results discussed in the article include enhancements of the singquandle counting invariant by the singquandle cocycle invariant, the singquandle polynomial invariant, and the singquandle shadow polynomial invariant.

The article also includes results involving psyquandles, which Ceniceros says “can be thought of as a generalization of singquandles.” The results covered include the psyquandle counting invariant and the Boltzmann weight enhancement of the psyquandle counting invariant.

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