Shen Lu

Research Interests

My research is in the general areas of operator algebras and noncommutative geometry. I am interested in studying C*-algebras associated to specfic non-finitely generated groups. Currently, I am working on classifying noncommutative solenoids (a family of twisted group C*-algebras) up to Morita-Rieffel equivalence by studying modules over these C*-algebras. Some of the key tools are from K-theory, Hilbert C*-modules, group theory, and p-adic analysis. Noncommutative solenoids also play a role in certain aspects of the noncommutative geometry of Alain Connes.

Selected Talks

• Irrational noncommutative solenoids and their finitely generated projective modules, C*-Seminar, Arizona State University, Feubuary 17, 2021 (slides)
• Minimal dynamical systems and C*-algebras, Math Colloquium, Metropolitan State University of Denver, October 2, 2020 (slides)
• Constructing finitely generated projective modules for noncommutative solenoids, 2020 Joint Mathematics Meetings in Denver, CO, January 18, 2020 (slides)
• Noncommutative solenoids and their finitely generated projective modules, Functional Analysis seminar, University of Colorado Boulder, October 17, 2019.

Publications

• Constructing equivalence bimodules between noncommutative solenoids: a two-pronged approach. ArXiv e-prints. arXiv:2103.02179
• (with C. Doran and B. R. Smith) New algorithms for modular inversion and representation by the form x^2 + 3xy + y^2, Involve: a Journal of Mathematics, Volume 10, Issue 4, April 2017, pages 541-554. (A paper from a summer research project Christina Doran and I contributed on while at Lebanon Valley College. Dr. Barry R. Smith was our project advisor.)