Monoidal Triangular Geometry with Applications to Representation Theory

Explore the historical background and recent developments in tensor triangular geometry and support theory for representations in this 45-minute conference talk. Delve into the origins of the subject, tracing its roots to the work of Alperin and Carlson in the late 1970s and 1980s, and examine the significant milestone of Paul Balmer's introduction of tensor triangular geometry in the mid-2000s. Discover the modern advancements in tensor categories and the recent development of a noncommutative version of Balmer's tensor triangular geometry by Nakano, Vashaw, and Yakimov. Learn about the framework for prime, semiprime, and completely prime (thick) ideals of a monoidal triangulated category, and understand the concept of the non-commutative Balmer spectrum. Focus on applications to studying the geometry around finite-dimensional Hopf algebras, gaining insights from this joint work with Kent Vashaw and Milen Yakimov.