p∗-Theory and modular representation theory

Ghosts in Modular Representation Theory

A ghost over a finite p-group G is a map between modular representations of G which is invisible in Tate cohomology. Motivated by the failure of the generating hypothesis—the statement that ghosts between finite-dimensional G-representations factor through a projective—we define the ghost number of kG to be the smallest integer l such that the composite of any l ghosts between finite-dimensiona...

Modular Representation Theory and the CDE Triangle

Perverse sheaves and modular representation theory

This paper is an introduction to the use of perverse sheaves with positive characteristic coefficients in modular representation theory. In the first part, we survey results relating singularities in finite and affine Schubert varieties and nilpotent cones to modular representations of reductive groups and their Weyl groups. The second part is a brief introduction to the theory of perverse shea...

Modular Representation Theory and Phantom Maps

In this talk, I will introduce and motivate the main objects of study in modular representation theory, which leads one to consider the stable module category. Perhaps surprisingly, one can do homotopy theory in this setting, as the stable module category has the structure of a stable model category. Therefore, there is a very rich interplay between modular representation theory and stable homo...

A Brief Summary of Modular Representation Theory

This paper shall provide a brief summary of representation theory, with a focus on how the semi-simple case differs from the modular case. It will be assumed that the reader has a reasonable background in algebra, but not assuming an existing understand of representation theory.