Metrics and approximability for triangulated categoriesMPIM

by Kabeer Rahul (MPIM)

Wednesday May 6, 2026, 2:00 PM → 3:45 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Seminar Room (Max Planck Institute for Mathematics)

Course on Metric and approximability for triangulated categories

Course Description: Neeman has recently introduced certain new techniques in the study of triangulated categories. These have been used to prove many important results, and have settled multiple open problems in algebraic geometry. In this course, we will discuss both these abstract techniques, and the growing body of works related to them along with several applications. In particular, we will introduce good metrics, completions, approximable triangulated categories, and see their various properties. Further, we will discuss applications to the non-existence of bounded t-structures, Rouquier dimension, semiorthogonal decompositions, representability results and so on. Most of the examples and applications in the course will be to algebraic geometry, but we note here that there are wider applications of the theory to representation theory and homotopy theory. See https://kabeermr.github.io/CourseOutline.pdf for the course outline.

Prerequisites: Some familiarity with derived and triangulated categories, and rudimentary knowledge of algebraic geometry.