Publications
Publications with students (at the time) are marked with *. In mathematics author order is always alphabetical.
Quantum Invariants and Quantum Algebra
Kashiwara-Vergne solutions degree by degree, with Iva Halacheva, Guillaume Laplante-Anfossi and Marcy Robertson, 2023 preprint arXiv:2310.20420.
A knot-theoretic approach to comparing the Grothendieck-Teichmüller and Kashiwara-Vergne groups*, with Tamara Hogan and Marcy Robertson, 2022 preprint arXiv:2211.11370.
A topological characterisation of the Kashiwara-Vergne groups, with Iva Halacheva and Marcy Robertson, Transactions of the American Mathematical Society 376-5 (2023) 3265–3317; arXiv:2106.02373.
Over then Under Tangles, with Dror Bar-Natan and Roland van der Veen, Special Issue in Memory of Vaughan Jones of J. Knot Theory Ramifications, 32-8 (2023) 2340003; arXiv:2007.09828.
Circuit Algebras are Wheeled Props, with Iva Halacheva and Marcy Robertson, Journal of Pure and Applied Algebra 225-12, (2021); arXiv:2009.09738.
Ribbon 2-knots, 1+1=2, and Duflo’s Theorem for Arbitrary Lie Algebras*, with Dror Bar-Natan and Nancy Scherich, Algebraic and Geometric Topology 20 (2020) 3733–3760; arXiv:1811.08558.
Finite Type Invariants of w-Knotted Objects II: Tangles, Foams and the Kashiwara– Vergne Conjecture, with Dror Bar-Natan, Math. Annalen 367(3-4) (2017) 1517–1586; arXiv:1405.1955.
Finite Type Invariants of w-Knotted Objects I: w-Knots and the Alexander Polynomial, with Dror Bar-Natan, Algebraic and Geometric Topology 16 (2016) 1063–1133; arXiv:1405.1956.
A Homomorphic Expansion for Knotted Trivalent Graphs, with Dror Bar-Natan, Journal of Knot Theory and its Ramifications, 22-1, (2013); arXiv:1103.1896.
Pentagon and Hexagon Equations Following Furusho, with Dror Bar-Natan, Proceedings of the American Mathematical Society 140 (2012), 1243-1250; arXiv:1010.0754.
On the Extension of the Kontsevich Integral to Knotted Trivalent Graphs, Algebraic and Geometric Topology 10 (2010), 1317–1365; arXiv: 0811.4615.
Combinatorics, Topology and Categorification
Mutation, surface graphs, and alternating links in surfaces*, with Hans Boden, Damian Lin and Tilda Wilkinson-Finch, 2023 preprint, arXiv:2306.08971.
Deletion-Contraction Triangles for Hausel-Proudfoot Varieties, with Michael McBreen and Vivek Shende, Journal of the European Mathematical Society, online first, (2023) arXiv:1910.00979.
Lattice of integer flows and the poset of strongly connected orientations for regular matroids*, with Jongmin Lim, Discrete Mathematics 346-12 (2023), 113589; arXiv:2202.13265.
Arc diagrams on 3−manifold spines*, with Jack Brand, Ben Burton, Alexander He, Adele Jackson and Joan Licata, Journal of Discrete and Computational Geometry (2023), arXiv:2202.02007.
Koszul Algebras and Flow Lattices, with Anthony Licata, Journal of Combinatorial Theory Series A 185 (2022) 105534; arXiv:1905.03067.
Odd Khovanov Homology for Hyperplane Arrangements, with Anthony Licata, Journal of Algebra 436, (2015), 102–144; arXiv:1205.2784.
Education
“You’ll Never Get Cultural Competence in Science”: an Australian Perspective on Integrating Cultural Competence into Science Teaching via Cultural Accountability, Cross, R., Quinnell, R., Bell, T., Rhodes, P., Dancso, Z., Hubble, T., Wardle, G., Lewis, M., Motion, A., Murphy, D., and Gongora, J, International Journal of Innovation in Science and Mathematics Education 29-3 (2021) 62–74.
Expository and Theses
What Is a Singular Knot? Chapter in: Encyclopedia of Knot Theory, CRC Press, 2020, Editors Colin Adams, Erica Flapan, Allison Henrich, Louis Kauffman, Lew Ludwig, and Sam Nelson.
Flying Rings and the Kashiwara–Vergne Problem, Oberwolfach Conference Report 42/2014, 2384–2387.
On a Universal Finite Type Invariant of Knotted Trivalent Graphs, University of Toronto PhD Thesis.
Edge Crossings in Combinatorial Geometry, Eotvos University Master’s Thesis, in Hungarian.