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
Summary of our activities in the year: 2021 ,
2022
Reports:

Papers submmited or accepted for publication:

S. Breaz:
On a theorem of Stelzer for some classes of mixed groups;
Mediterr. J. Math., 19 (4) paper no. 159 (2022), 14 pp.

S. Breaz, T. Brzeziński, B. Rybołowicz, P. Saracco:
Heaps of modules and affine spaces;
arXiv

S. Breaz, Y. Zhou:
When is every non centralunit a sum of two nilpotents?;
to appear in Contemporary Math.;
arXiv

Cs. Szanto, I. Szollosi:
RingelHall polynomials associated to a quiver of type $\tilde D_4$

S. Breaz, M. Hrbek, C.G. Modoi:
Silting, cosilting, and extensions of commutative ring;
arXiv

S. Breaz, A. Marcus, C.G. Modoi:
Support τtilting modules and semibricks over group graded algebras
arXiv

Cs. Szanto, I. Szollosi:
RingelHall polynomials associated to tame indecomposable modules of defect 2,1,0,1,2;
submitted 2022

S. Breaz, C. Rafiliu:
Decompositions of matrices by using commutators;
arXiv

Preprints:

S. Breaz, C.G. Modoi:
Migration of silting objects via adjoint pairs

S. Breaz, F. Pop:
On extriangulated categories
Visits, conferences, workshops

S. Breaz:
Homological Methods in Representation Theory. A conference in honour of Lidia Angeleri Hugel;
03  08 October 2021;
Fraueninsel (Chiemsee), Abtei Frauenworth, Germany;
Talk: Transfer of homological properties along some canonical functors.

C.G. Modoi:
Homological Methods in Representation Theory. A conference in honour of Lidia Angeleri Hugel;
03  08 October 2021;
Fraueninsel (Chiemsee), Abtei Frauenworth, Germany.

Cs. Szanto:
Algebra Seminar of Renyi Institute;
07 March 2022;
Budapest, Hungary;
Talk: RingelHall polynomials associated to a quiver of type $\tilde{D}_{4}$.

S. Breaz:
Malga Seminar PadovaVerona, Universita di Verona;
24 May 2022;
Talk: Silting complexes and extensions of commutative rings.

S. Breaz:
Functor Categories, Model Theory, and Constructive Category Theory, Universidad de Almeria;
1115 July 2022;
Talk: Change of scalars functors and silting complexes.

C.G. Modoi:
Functor Categories, Model Theory, and Constructive Category Theory, Universidad de Almeria;
1115 July 2022;
Talk: Not necessarily compact approximability via silting theory.

S. Breaz:
Hopf algebras, monoidal categories and related topics;
2729 July 2022;
IMAR, Bucharest, Romania;
Talk: Heaps of Modules.

A. Marcus:
Hopf algebras, monoidal categories and related topics;
2729 July 2022;
IMAR, Bucharest, Romania;
Talk: Tilting complexes over a Ggraded Galgebra.

T. Micu:
Young Researchers' Conference on NonArchimedean and Tropical Geometry;
0105 August 2022;
Universität Regensburg;
Talk: The structure of special fibers through valuations.

T. Micu:
Representation Theory and Triangulated Categories;
2630 September 2022;
Paderborn, Germany.

V.A. Minuță:
Representation Theory and Triangulated Categories;
2630 September 2022;
Paderborn, Germany.

C.G. Modoi:
Representation Theory and Triangulated Categories;
2630 September 2022;
Paderborn, Germany.

S. Breaz:
Algebra Seminar of Charles University;
1012 October 2022;
Prague, The Czech Republic;
Talk: The BaerKaplansky Theorem and Heaps of Modules.
Contact
email:
username: bodo 
server: math.ubbcluj.ro 
username: ssbreaz 
server: gmail.com 
fax:
+40 264 691906
adresa:
Simion Breaz
"BabeșBolyai" University
Faculty of Mathematics and Computer Science
Str. Mihail Kogălniceanu nr. 1
RO400084 ClujNapoca
Romania