Research

My research area is generally in algebra and geometric group theory. I am mainly interested in geometric and combinatorial aspects of Coxeter groups, as well as closely related objects like Artin groups and Hecke Algebras. Recently, I have also developed an interest in applying statistics and machine learning in the study of historical cryptology.

Papers and Preprints

• Ultra-Low elements and Join Irreducible gates in Coxeter Groups.
  (Y. Yau)
  Submitted (2025) pdf

• A pair of Garside shadows.
  (P. Przytycki, Y. Yau)
  Algebraic Combinatorics, vol 7, no. 6, p1879-1885 (2024) pdf

• An artificial neural network approach to finding the key length of the Vigenère cipher.
  (C. Millichap, Y. Yau)
  Cryptologia, 1-17 (2023) pdf

• Modifying twist algorithms for determining the key length of a Vigenère cipher.
  (C. Millichap, Y. Yau, A. Pate, M. Carns)
  Cryptologia, 1-16 (2023) pdf

• Cone types, automata, and regular partitions in Coxeter groups.
  (J. Parkinson, Y. Yau)
  Advances in Mathematics, vol 398 (2022) pdf

• Coxeter Systems for which the Brink-Howlett automaton is minimal.
  (J. Parkinson, Y. Yau)
  Journal of Algebra, vol 527, p437-446 (2019) pdf

Other

• Automatic structures for Coxeter groups.
  (Y. Yau)
  PhD Thesis, University of Sydney (2021) link