Silting objects and t-structures in derived categories I,II,III

Abstract: The notion of silting, generalising tilting, has been in the
literature for over twenty years. Recent work by Aihara, Bondarko,
Iyama, Keller, Koenig, Nicolas, Yang has shown deep connections of
these objects with t-structures and  co-t-structures in certain
triangulated categories. In these talks we explore some of these
connections and discuss important operations/constructions with
silting objects, namely silting mutation and glueing with respect to a

In the first talk, we will discuss the fundamental concept of
t-structure. Certain collections of objects, ranging from
simple-minded objects to ext-projectives in the aisle, will be
discussed, as they parametrise suitable classes of t-structures in
derived module categories. Moreover, we will recall an operation,
namely the HRS-tilting, on t-structures.

In the second talk, the connections between silting objects and
structures in triangulated categories will be made explicit. Silting
mutation will be introduced and compared with HRS-tilting.

In the third talk, we will focus on glueing with respect to a
recollement. Ranging from t-structures to co-t-structures, glueing
techniques can be extended in a compatible way to silting objects.
Moreover, we show that in the piecewise hereditary setting, all
silting objects are obtained through this process.