Research

Code that I use in my work is available at github.com/mrhmath.

Publications

  1. Matthew Harper, Ben-Michael Kohli.
    The Links--Gould polynomial of an alternating link is alternating.
    arXiv:2610.18803
  2. Matthew Harper, Ben-Michael Kohli.
    The colored Jones function does not determine any colored Links--Gould polynomial.
    arXiv:2610.12352
  3. Vladimir Chernov, Matthew Harper, Ben-Michael Kohli.
    Detecting causality with the Links--Gould polynomial.
    arXiv:2605.15515
  4. Matthew Harper, Thomas Kerler.
    Hopf ideals, integrality, and automorphisms of quantum groups at roots of 1.
    arXiv:2512.23503
  5. Matthew Harper, Ben-Michael Kohli, Jiebo Song, Guillaume Tahar.
    On some log-concavity properties of the Alexander-Conway and Links--Gould invariants.
    arXiv:2509.16868
  6. Stavros Garoufalidis, Matthew Harper, Rinat Kashaev, Ben-Michael Kohli, Emmanuel Wagner.
    On the colored Links--Gould polynomial.
    arXiv:2509.10911
  7. Matthew Harper, Efstratia Kalfagianni.
    On the quantum \(\mathfrak{sl}_3\) invariant of positive links.
    To appear in Algebraic & Geometric Topology. arXiv:2508.15153
  8. Stavros Garoufalidis, Matthew Harper, Rinat Kashaev, Ben-Michael Kohli, Jiebo Song, Guillaume Tahar.
    Skein theory for the Links--Gould polynomial.
    Journal of the London Mathematical Society (2026). arXiv:2505.19251
  9. Stavros Garoufalidis, Matthew Harper, Ben-Michael Kohli, Jiebo Song, Guillaume Tahar.
    Extending knot polynomials of braided Hopf algebras to links.
    SIGMA: Symmetry, Integrability, Geometry: Methods and Applications (2026). arXiv:2505.01398
  10. Francesco Costantino, Matthew Harper, Adam Robertson, Matthew B. Young.
    Non-semisimple topological field theory and \(\hat{Z}\)-invariants from \(\mathfrak{osp}(1|2)\).
    Letters in Mathematical Physics (2026). arXiv:2407.12181
  11. Matthew Harper, Peter Samuelson.
    The Temperley--Lieb tower and the Weyl algebra.
    Journal of the London Mathematical Society (2025). arXiv:2401.02545
  12. Matthew Harper.
    A non-abelian generalization of the Alexander polynomial from quantum \(\mathfrak{sl}_3\).
    SIGMA: Symmetry, Integrability, Geometry: Methods and Applications (2026). arXiv:2008.06983
  13. Matthew Harper.
    Seifert--Torres type formulas for the Alexander polynomial from quantum \(\mathfrak{sl}_2\).
    Topology and its Applications (2022). arXiv:1911.00646
  14. Matthew Harper.
    Verma modules for restricted quantum groups at a fourth root of unity.
    arXiv:1911.00641

Undergraduate Publications

  1. Matthew Harper, Larry Zamick.
    Scissors mode from a different perspective.
    Physical Review C (2015). arXiv:1501.03788
  2. Shadow J. Q. Robinson, Castaly Fan, Matthew Harper, Larry Zamick.
    On the vibrational model of \(^\text{92}\)Pd and comparison with \(^\text{48}\)Cr.
    International Journal of Modern Physics E (2021). arXiv:1411.1390
  3. Larry Zamick, Yitzhak Y. Sharon, Shadow J. Q. Robinson, Matthew Harper.
    Consequences of omitting spin-orbit partner configurations for \(B(E2)\) values and quadrupole moments in nuclei.
    Physical Review C (2015). arXiv:1410.6145
  4. Matthew Harper, Larry Zamick.
    \(J = 0, T = 1\) pairing-interaction selection rules.
    Physical Review C (2015). arXiv:1408.4016
  5. Larry Zamick, Matthew Harper.
    Wave functions of the \(Q\cdot Q\) interaction in terms of unitary 9-\(j\) coefficients.
    Physical Review C (2015). arXiv:1306.4661