**Speaker:** Jonathan Gruber (Lausanne)

**Title:** *Singular Modules for Reductive Algebraic Groups and a Translation Principle for Tensor Products*

**Abstract:**

Let \(G\) be a connected reductive algebraic group over an algebraically closed field of positive characteristic. In this talk, I will introduce the notion of 'negligible tilting modules' and explain how one can use complexes of negligible tilting modules to define a tensor ideal of 'singular \(G\)-modules'. This tensor ideal can then be used to establish a 'translation principle for tensor products'. Much like Jantzen's (ordinary) translation principle, this allows one to (partially) reduce the study of the monoidal structure of the category of finite-dimensional rational G-modules to the study of tensor products of modules in the principal block of \(G\).