Title: Silting theory
Speaker: Jorge Vitória
Silting modules generalise tilting modules over any ring and support
tau-tilting modules over a finite dimensional algebra. In this talk,
we explore some properties of silting theory and show how silting
modules relate with quasitilting modules. Furthermore, we discuss the
connection between silting modules and silting complexes in the
derived category, which are themselves intimately related with
t-structures and co-t-structures. This is joint work with Lidia
Angeleri Hügel and Frederik Marks.
Title: Silting modules and ring epimorphisms
Speaker: Frederik Marks
In the first part of the talk we discuss ring epimorphisms that arise
from partial silting modules. These ring epimorphisms are described
explicitly by a certain quotient of the endomorphism ring of the
completion of the partial silting. This description allows us to
relate the representations theories of the initial ring and the
endomorphism ring of a given silting module.
In the second part of the talk we restrict the setting to tilting.
More precisely, we define (strongly) minimal tilting modules over a
ring and show that there is a way of assigning to every such tilting
module a ring epimorphism using the construction discussed in the
first part. For hereditary rings the map obtained yields a bijection
between strongly minimal tilting modules and injective homological
ring epimorphisms. This is joint and ongoing work with
Lidia Angeleri Hügel and Jorge Vitória.