Speaker
Description
For a finite-dimensional algebra A, the category mod(A) can be
recovered inside the bounded derived category of A as the full
subcategory of objects whose cohomology is concentrated in degree 0. A
natural enlargement is obtained by considering, for a fixed n>0, those
objects whose cohomology is concentrated in degrees 1-n,...,0. This
subcategory is called the n-extended heart of the standard t-structure.
For n=1, one recovers the abelian category mod(A), while for n>1 the
extended heart is no longer abelian. Nevertheless, it retains many
features reminiscent of module categories; for example, it admits
Auslander--Reiten sequences. I will explain why extended hearts are
useful for studying finite-dimensional algebras and their derived analogues.