This volume contains the proceedings of the conference Recent Advances and New Directions in the Interplay of Noncommutative Algebra and Geometry, held from June 20-24, 2022, at the University of Washington, Seattle, in honor of S. Paul Smith's 65th birthday. The articles reflect the wide interests of Smith and provide researchers and graduate students with an indispensable overview of topics of current interest. Specific fields covered include: noncommutative algebraic geometry, representation theory, Hopf algebras and quantum groups, the elliptic algebras of Feigin and Odesskii, Calabi-Yau algebras, Artin-Schelter regular algebras, deformation theory, and Lie theory.
In addition to original research contributions the volume includes an introductory essay reviewing Smith's research contributions in these fields, and several survey articles.
Jason P. Bell, Leon Burkhardt, and Nicholas Priebe, Ore extensions of
commutative rings and the Dixmier-Moeglin equivalence
Raf Bocklandt and Jasper van de Kreeke, Deformations of gentle
$A_\infty$-algebras
K. A. Brown and J. T. Stafford, The prime spectrum of the Drinfeld double of
the Jordan plane
Alex Chirvasitu, Ryo Kanda, and S. Paul Smith, Modular properties of elliptic
algebras
K. R. Goodearl, Spectra of quantum algebras
Timothy J. Hodges, Introduction to Belavin-Drinfeld quantum groups
Hongdi Huang, Xin Tang, and Xingting Wang, A survey on Zariski cancellation
problems for noncommutative and Poisson algebras
Colin Ingalls and Takehiko Yasuda, Log centres of noncommutative crepant
resolutions are Kawamata log terminal: Remarks on a paper of Stafford and Van
den Bergh
Ian M. Musson, On the geometry of some algebras related to the Weyl groupoid
Pablo S. Ocal, Kenta Ueyama, and Padmini Veerapen, A primer on twists in the
noncommutative realm focusing on algebra, representation theory, and
geometry
Daniel Rogalski, Artin-Schelter regular algebras
Hung V. Tran and Michaela Vancliff, Twisting systems and some quantum
$\mathbb{P}^3$s with point scheme a rank-2 quadric
Michaela Vancliff, An example of a quadratic AS-regular algebra without any
point modules
K. A. Brown, University of Glasgow, United Kingdom, T. J. Hodges, University of Cincinnati, OH, M. Vancliff, University of Texas at Arlington, TX, and J. J. Zhang, University of Washington, Seattle, WA.
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