A quandle coloring quiver is a quiver structure, introduced by Karina Cho and Sam Nelson, and defined on the set of quandle colorings of an oriented knot or link with respect to a finite quandle. In this talk, we study quandle coloring quivers of 
In this talk we discuss pseudoknots and singular knots. Specifically, we discuss psyquandles and their application to oriented pseudoknots and oriented singular knots. Additionally, we bring cocycle enhancement theory to the case of psyquandles to define enhancements of the psyquandle counting invariant via pairs of a biquandle 2-cocycle and a new function. As an application, we define a single-variable polynomial invariant of both oriented pseudoknots and oriented singular knots.
In this talk I recall the definitions of shelf/rack/quandle and their cohomology theory. I also give the construction of cocycle invariant of links, due to Carter, Jelsovsky, Kamada, Langford and Saito (Trans. Amer. Math. Soc. 355 (2003), 3947-3989). Then, I introduce higher arity self-distributive structures and show that an appropriate diagrammatic interpretation of them is suitable to define a ternary version of the cocycle invariant for framed link invariants, via blackboard framings. I discuss the computation of cohomology of ternary structures, as composition of mutually distributive operations, and a cohomology theory of certain ternary quandles called group heaps. Furthermore I mention a categorical version of self-distributivity, along with examples from Lie algebras and Hopf algebras, and the construction of ribbon categories from ternary operations that provide a quantum interpretation of the (ternary) cocycle invariant.
Elhamdadi, Mohamed, Masahico Saito, and Emanuele Zappala. “Higher Arity Self-Distributive Operations in Cascades and their Cohomology.” arXiv preprint arXiv:1905.00440 (2019).
Elhamdadi, Mohamed, Masahico Saito, and Emanuele Zappala. “Heap and Ternary Self-Distributive Cohomology.” arXiv preprint arXiv:1910.02877 (2019).
Zappala, Emanuele. “Non-Associative Algebraic Structures in Knot Theory.” (2020).