Hazewinkel wrote [this article][1] in 2005. Perhaps it's time for an update.

For example, updating item

**34: Ordinary differential equations** much work has been done on the underlying Hopf algebra (HA) of Lie-Butcher numerical methods for solving autonomous and non-autonomous ODE's (evolution equations) by , e.g., Ebrahimi-Fard, Hans Munthe-Kaas and their colleagues. See, e.g.,

i) "[Butcher series][2]: A story of rooted trees and numerical methods for evolution equations" by McLachlan, Modin, Munthe-Kaas, and Verdier

ii) "Lie-Butcher series, Geometry, Algebra and Computation" by Munthe-Kaas ander K. Føllesdal

This is closely allied to item

**81: Quantum theory**

through the HA (combinatorial Faa di Bruno bialgebra, trees, Feynman diagrams) of renormalization to which Alain Connes, Christian Brouder, David Broadhurst, Dirk Kreimer, Kurush Ebrahimi-Fard, Hector Figueroa, Jose Gracia-Bondia, Hans Munthe-Kass, Loic Foissy, Karen Yeats, Paul-Hermann Balduf, et al. have contributed.  




   
  


  [1]: https://arxiv.org/abs/math/0411536
  [2]: https://arxiv.org/abs/1512.00906