6 papers
Thompson's Group and Virtual Link Theory
Micah Chrisman, Louisa Liles, Melody Molander
Thompson's groups were introduced in 1965 and have since found widespread application in fields as diverse as logic, group theory, homotopy theory, and latt…
NIM-representations of Tambara-Yamagami generalizations
Agustina Czenky, Emily McGovern, Melody Molander +2
We compute and classify the irreducible non-negative integer matrix (NIM-)representations of two proposed generalizations of the Tambara-Yamagami fusion ring, as studied by Jordan-…
A mirror deformation of Markov numbers
Léa Bittmann, Perrine Jouteur, Ezgi Kantarcı Oğuz +2
We introduce a deformed squared Markov equation given by . Symmetric solutions of this new equation present a remarka…
A Well-Defined Jellyfish Algorithm for the Affine Subfactor Planar Algebra
Melody Molander
In this paper, we contribute to the Kuperberg program by giving a diagrammatic presentation of generators and relations for the affine unshaded subfactor planar algebra. Usin…
Skein Theory for Affine A Subfactor Planar Algebras
Melody Molander
The Kuperberg Program asks to find presentations of planar algebras and use these presentations to prove results about their corresponding categories purely diagrammatically. This…
A determinant formula of the Jones polynomial for a family of braids
Derya Asaner, Sanjay Kumar, Melody Molander +2
In 2012, Cohen, Dasbach, and Russell presented an algorithm to construct a weighted adjacency matrix for a given knot diagram. In the case of pretzel knots, it is shown that after…