RESEARCH
My research centers on the interface of algebra, topology, and combinatorics. I am mainly interested in algebraic invariants of objects in low-dimensional topology such as knots and 3-manifolds. This also includes invariants of objects in graph theory or topological graph theory, such as graph polynomials and ribbon graph invariants.
PAPERS, PREPRINTS, AND PROCEEDINGS:
- W. Moltmaker & L. H. Kauffman, On Vassiliev Invariants of Virtual Knots (ArXiv)
- W. Moltmaker & R. I. van der Veen, New Quantum Invariants of Planar Knotoids (ArXiv)
- W. Moltmaker, Framed Knotoids and Their Quantum Invariants (Communications in Mathematical Physics, ArXiv)
- W. Moltmaker, A Hopf algebra approach to q-Deformation of Physics (Bachelor's Thesis, unpublished)
$\hat{W}_{\mathfrak{g},\rho} (\check{Z}(K)) = Q^{\mathfrak{g},\rho}(K)\big\vert_{q=e^{h/2}}$
$\mathfrak{g} = \mathfrak{h}\oplus \left(\bigoplus_{\alpha\in\Phi} \mathfrak{g}_\alpha\right)$
$\sum_{i\in\mathbb{Z}} (-1)^i \text{qdim}(KH^{i,j}(D)) = \hat{J}(D)$