MIT Infinite Dimensional Algebra Seminar
Friday, November 19, 2021 at 3:00pm to 5:00pm
Building 2, 2-135
182 MEMORIAL DR, Cambridge, MA 02139
Speaker: Kent Vashaw (MIT)
Title: On the spectrum and support of a finite tensor category
Abstract: The tools of support varieties (initiated by Carlson in 1983) and tensor triangular geometry (initiated by Balmer in 2005) have played an important role in the study of monoidal triangulated categories, with stable categories of finite tensor categories forming one of the principal classes of examples. The relationship between support varieties and tensor triangular geometry has been used in many cases to classify the thick ideals of the category in question, a fundamental problem. We will discuss work of Buan-Krause-Solberg and Nakano-V.-Yakimov, which defined and developed noncommutative versions of Balmer's theory, and will proceed to describe new methods for determining the Balmer spectrum and thick ideals of a monoidal triangulated category. This is joint work with Daniel Nakano and Milen Yakimov..
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