The term “spectra” is overused across different areas of mathematics, including topology, algebraic geometry, functional analysis etc. This naturally raises the question: is there a way to “relate” these various spectra, or even develop a unified framework to study them? Luckily, there is a good approach called the “tensor triangulated geometry”, or tt-geometry, founded by Paul Balmer in the 2000s, provides an insightful way to do that in a certain sense. Broadly speaking, tt-geometry is the study of tensor triangulated categories by algebro-geometric methods. This perspective has led to many classification results in many areas of math, like algebraic geometry, homotopy theory, representation theory, or even C^*-algebra. In this talk, I will introduce the core idea of this approach, and provide some illustrative examples. If time permits, I will also discuss some developments and potential directions in this area. The only prerequisites are graduate-level knowledge in algebra, topology, and category theory. Familiarity with triangulated categories would be helpful but not necessary, as I will outline the essential ideas.
Graduate Student Geometry-Topology Seminar
Friday, February 21, 2025 - 2:00pm
Albert Yang
University of Pennsylvania
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