# Semibricks in $\tau$-tilting theory

This talk is based on my paper "Semibricks" in IMRN.

In representation theory of a finite-dimensional algebra $A$ over a field $K$, bricks and semibricks are fundamental and useful notions.

Here, a brick means an $A$-module whose endomorphism ring is a division $K$-algebra, and a semibrick means a set of bricks which are pairwise Hom-orthogonal, so (semi)bricks are a generalization of (semi)simple modules.

I study semibricks from the point of view of $\tau$-tilting theory.

I proved that there is a one-to-one correspondence between the support $\tau$-tilting modules and the semibricks satisfying a certain condition called left finitess.

Also, I introduced brick labels for the exchange quiver of the support $\tau$-tilting modules by using this bijection.

I would like to explain these results and the new perspective of $\tau$-tilting theory

given by them.

This seminar will be hold at RIMS 006.