# Manin-Schechtman theory and Soergel bimodules

SPEAKER: Benjamin Elias

TITLE: Manin-Schechtman theory and Soergel bimodules

ABSTRACT: There is one indecomposable Soergel bimodules for each element of the symmetric group, but they sure are hard to find! In order to find the idempotent which picks out the indecomposable bimodules as a summand of an easier bimodule, it will be useful to study the set $Gamma_w$ of reduced expressions of a given permutation $w$. This gives an excellent excuse to lecture on Manin-Schechtman theory, which places the structure of a partially oriented graph on $Gamma_w$. This orientation is in some sense a “higher Bruhat order.” Manin-Schechtman theory illustrates one of the most astonishing and beautiful features of the symmetric group, which seems to be intrinsically linked to the Soergel category.