Contains the proceedings of the conference Recent Advances and New Directions in the Interplay of Noncommutative Algebra and Geometry, held in June 2022, at the University of Washington, Seattle, in honor of S. Paul Smith's 65th birthday. The articles reflect Smith’s wide interests and provide an indispensable overview of topics of interest.

Jason P. Bell, Leon Burkhardt, and Nicholas Priebe, Ore extensions of commutative rings and the Dixmier-Moeglin equivalenceRaf Bocklandt and Jasper van de Kreeke, Deformations of gentle $A_\infty$-algebrasK. A. Brown and J. T. Stafford, The prime spectrum of the Drinfeld double of the Jordan planeAlex Chirvasitu, Ryo Kanda, and S. Paul Smith, Modular properties of elliptic algebrasK. R. Goodearl, Spectra of quantum algebrasTimothy J. Hodges, Introduction to Belavin-Drinfeld quantum groupsHongdi Huang, Xin Tang, and Xingting Wang, A survey on Zariski cancellation problems for noncommutative and Poisson algebrasColin Ingalls and Takehiko Yasuda, Log centres of noncommutative crepant resolutions are Kawamata log terminal: Remarks on a paper of Stafford and Van den BerghIan M. Musson, On the geometry of some algebras related to the Weyl groupoidPablo S. Ocal, Kenta Ueyama, and Padmini Veerapen, A primer on twists in the noncommutative realm focusing on algebra, representation theory, and geometryDaniel Rogalski, Artin-Schelter regular algebrasHung V. Tran and Michaela Vancliff, Twisting systems and some quantum $\mathbb{P}^3$s with point scheme a rank-2 quadricMichaela Vancliff, An example of a quadratic AS-regular algebra without any point modules