Charles Paquette, Royal Military College of Canada
Title: Bricks and tau-rigid modules and their interaction

For a finite dimensional algebra A, let ind(A) denote the set of isoclasses of indecomposable modules in mod(A). We consider the subsets brick(A) and i\tau-rigid(A) of ind(A) consisting of bricks and \tau-rigid modules, respectively. We show that every brick over A is tau-rigid if and only if A is locally representation directed. In this case, we get ind(A) = brick(A) = i\tau-rigid(A). This extends a result obtained by P. Draexler. We also study the geometric counterpart of this phenomenon at the level of irreducible components of module varieties. Namely, we study indecomposable, brick and generically \tau-reduced irreducible components and explain what happens when some of these classes coincide. A special attention is given to E-tame algebras (which include tame algebras). This is a report on a joint work with Kaveh Mousavand.