I also have a habit of coorganizing graduate student topics seminars on various subjects related to Representation theory (notes available!):
In Fall 2018, I've coorganized a graduate student seminar on perverse sheaves. See here for details.
In Fall 2017, I've coorganized a graduate student seminar on Category O and Soergel bimodules. See here for details.
In the Spring 2017 I've coorganized DAHAEHA (Double Affine Hecke Algebras and Elliptic Hall Algebras) seminar.
In the Spring 2016 I've coorganized MIT-NEU graduate student seminar on moduli spaces of sheaves on K3 surfaces. Here are the details.
In the Spring 2015, we were discussing various things related to quiver varities. This was accompanied by several invited lectures by Raphael Rouquier (UCLA), Andrei Okounkov (Columbia) and Dmitry Kaledin (Steklov Institute).
In the Fall 2014, we were focussing on Hecke algebras.
In the Spring 2014, we discussed various geometric and representation theoretic questions related to the Hilbert scheme of points on the plane.
In the Fall 2013 we did our best to study connections between quantum cohomology and representation theory in the setting of cotangent bundles to flag varieties.