Department of Mathematics, Faculty of Mathematics and Computer Science, "BabeșBolyai" University, ClujNapoca
Research Project: "Contributions to Silting Theory"
Code: 
PNIIIP4IDPCE20200454 
Contract: 
75/04.01.2021 
Period: 
January 2021December 2023 
Financed by: 
Unitatea Executivă pentru Finanțarea Învățământului
Superior, a Cercetării, Dezvoltării și Inovării UEFISCDI

 Team
 Abstract
 Results
 Research visits, conferences, workshops
 Contact
Team:
Abstract:
The main aim is to study (co)silting objects which can be associated to
some categories, as module categories over some particular rings,
Grothendieck or triangulated categories.

SCIENTIFIC OBJECTIVES:

Contributions to silting theory. The main topics will be the following:

Silting and cosilting complexes in the derived categories.
Structures related to these mathematical objects.

The transfer of the (co)silting properties via functors.

Special classes and objects. The topics are the following:

Approximations and definable classes.
We will study preenveloping and precovering classes induced by (co)silting objects.

Pureinjective objects in Grothendieck and triangulated categories.
We will try to use some triangulated versions for the classical notion of
pfunctor in order to obtain new information about the class of pureinjective objects.

ADMINISTRATIVE OBJECTIVES:

Completion of the research
infrastructure by assuring the bibliographical background (books,
journals) and the material background of the research (computers, office
consumables etc.)

Improving the level of knowledge of the team
members and other young researchers and students.

RESEARCH SEMINARS:
(S1) Silting objects in module theory (silting, cosilting and ttilting modules)
(S2) Silting objects in triangulated categories
(S3) Splitting properties and the structure of (pure) projective and (pure) injective modules.
(S4) Identities in rings and approximations
Reports of our activities: 2021 ,
2022 , 20212023 ,
20212023 (in Romanian)
Results:
Summary: Our results concern several settings:
the general theory of silting objects in triangulated categories as well as some particular situations
(derived categories over commutative rings or dgalgebras, or $\tau$tilting theory for some generalizations of group algebras)
which require specific approach and special techniques.
Our team members investigations also provided results on module categories over finite dimensional algebras
(like group algebras or path algebras over some special quivers)
or on some methods to associate affine structures to module categories.