15:30-16:30 Diego Barceló Nieves
Title: On (Co)silting
Bijections Involving the Category of Large Projective
Presentations
Abstract: Based on results by Adachi-Iyama-Reiten,
Marks-Šťovíček, Pauksztello-Zvonareva and Adachi-Tsukamoto,
García successfully completed a commutative 'triangular prism'
of bijections connecting the classes of support tau-tilting
modules, functorially-finite torsion pairs and left finite wide
subcategories in the category of
finitely-generated A-modules—where A is a finite-dimensional
algebra over an algebraically closed field—to the classes of
'silting objects', complete cotorsion pairs and thick
subcategories with enough injectives in the category of
projective presentations of objects in mod(A)—which
has many powerful properties. In this talk,
we will present advances towards generalizing these results to
the realm of infinite-dimensional modules over more general
classes of rings—and, furthermore, dualizing them. It is based
on joint work in progress with Lidia Angeleri Hügel.
17:00-18:00 Enrico Sabatini
Title: Compactly generated
t-structures of path algebras over commutative Noetherian rings
Abstract: The problem of
characterising subcategories of the derived category of a
commutative Noetherian ring has been studied extensively in the
last thirty years. The most important results are the
characterisation of localising subcategories in terms of subsets
of Spec(R), the prime spectrum of the ring, due to A. Neeman in
1992, and the characterisation of compactly generated
t-structures in terms of chains of these subsets, due to L.
Alonso, A. Jeremías and M. Saorín in 2010. The first result was
generalised by B. Antieau and G. Stevenson in 2016 to the
derived category D(RQ) of representations of a quiver Q over a
commutative Noetherian ring R. In particular, they proved that a
characterisation of localising subcategories of D(RQ) in terms
of functions from Spec(R) to a set Nc(Q), depending on Q, holds
for any Dynkin quiver and commutative Noetherian ring. The aim
of this project is to find the corresponding generalisation of
the result concerning compactly generated t-structures. In this
talk I will give an overview of the history of this project,
introduce all the ingredients and show the results mentioned
above. Finally, I will talk about the new results and the
techniques that have been developed in order to solve the
problem in this general context.