Motivic tensor-triangular geometry, I

Abstract of mini-series: Tensor-triangular geometry is a geometric approach to certain classification problems in a wide variety of contexts, ranging from topology to representation theory and algebraic geometry. In a series of three talks we will introduce the audience to this approach, particularly geared towards the study of cohomological (or, "motivic") aspects of algebraic varieties. In the last few years, this has unearthed interesting structures in categories of motives which we will report.

 

Abstract of talk:
The talk will introduce the main players and the motivating problem of this three-part miniseries. We'll start by tracing the history of the "tt-classification problem", from topology through algebra, representation theory, and algebraic geometry. We'll then discuss the motivic theory as it concerns us here, and state the main objective of motivic tt-geometry.