My main research area is on operator algebra arising from various algebraic structures (semigroup, group, groupoids, graphs, etc) and their interactions. I am especially interested in the Zappa-Szep product construction in operator algebras. Recenly, I am interested in the application of operator theoretical techniques in the theory of neuron networks in machine learning.
Research profiles:
Dilation theory and semigroup representations
Marcelo Laca and Boyu Li, Dilation theory for right LCM semigroup dynamical systems, Journal of Mathematical Analysis and Application, 505(2), no. 125586, 2022
Boyu Li, Wold decomposition on odometer semigroups, Proceedings of the Royal Society of Edinburgh, 152(3):738-755, 2022
Boyu Li, C*-envelope and dilation theory of semigroup dynamical systems, Integral Equations and Operator Theory, 93 (3), no. 19, 2021
Marcelo Laca and Boyu Li, Amenability and functoriality of right-LCM semigroup C*-algebras. Proceedings of American Mathematical Society, 148(12):5209-5224, 2020
Boyu Li, Regular dilation and Nica-covariant representation on right LCM semigroups. Integral Equations and Operator Theory, 91(4), no. 36, 2019
Kenneth R. Davidson, Adam Dor-on and Boyu Li, Structure of Free Semigroupoid Algebras, Journal of Functional Analysis, 277(9):3283-3350, 2019
Boyu Li, Regular Dilation on Graph Products of N, Journal of Functional Analysis, 273(2):799-835, 2017
Boyu Li, Normal Extensions of Representations of Abelian Semigroups. Canadian Mathematical Bulletin, 59:564-574, 2016.
Boyu Li, Regular Representations of Lattice Ordered Semigroups, Journal of Operator Theory 76(1):33-56, 2016
Zappa-Szep product and self similar actions
Anna Duwenig and Boyu Li, The Zappa-Szep product of twisted groupoids, https://arxiv.org/abs/2406.00466
Anna Duwenig and Boyu Li, Imprimitivity theorems and self-similar actions on Fell bundles, Journal of Functional Analysis, 288(2), no. 110699, 2025
Boyu Li and Dilian Yang, Wold Decomposition and C*-envelopes of Self-Similar Semigroup Actions on Graphs, Journal of Mathematical Analysis and Application, 537(2), no. 128395, 2024
Anna Duwenig and Boyu Li, Equivalence of Fell bundles is an equivalence relation, Münster Journal of Mathematics 16(1):95-145, 2023
Boyu Li and Dilian Yang, Zappa-Szép actions of groups on product systems, Journal of Operator Theory, 88(2):247-274, 2022
Anna Duwenig and Boyu Li, The Zappa-Szép product of a Fell bundle and a groupoid, Journal of Functional Analysis, 282(1), no. 109268, 2022
Machine learning and neural network
Robert S. Fong, Boyu Li, and Peter Tiňo, Linear Simple Cycle Reservoirs at the edge of stability perform Fourier decomposition of the input driving signals. Chaos: An Interdisciplinary Journal of Nonlinear Science, 35(4), no. 043109, 2025
Robert S. Fong, Boyu Li, and Peter Tiňo, Universality of real minimal complexity reservoir, AAAI-25.
Boyu Li, Robert S. Fong, and Peter Tiňo, Simple Cycle Reservoirs are Universal, Journal of Machine Learning Research, 25(158):1−28, 2024.