Penn Arts & Sciences Logo

Graduate Student Geometry-Topology Seminar

Friday, February 21, 2025 - 2:00pm

Albert Yang

University of Pennsylvania

Location

University of Pennsylvania

DRL 4C8

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.

Other Events on This Day

There are no other events scheduled for this day.