Tensor triangular geometry for modular representation theory
Modular representation theory studies representations of a finite group and other algebraic structures such as Lie algebras over a field of positive characteristic. Classifying modular representation up to direct sums – as the classical theory does for complex representations – is often a hopeless task even for such a tiny group as Z/3 x Z/3. I’ll discuss a geometric approach to understanding this wild territory starting with D. Quillen’s classical work on mod p group cohomology and leading to the applications of the ideas of tensor triangular geometry of P. Balmer to modular representation theory.
Joint work with D. Benson, S. Iyengar and H. Krause.
Professor Julia Pevtsova, University of Washington