Research Project: "Contributions to Silting Theory"

(Versiune în Română)

1. Team
2. Abstract
3. Results
4. Research visits, conferences, workshops
5. Contact

Team:

• Simion Breaz
• Andrei Marcus
• Tudor Micu
• George Ciprian Modoi
• Cosmin Pelea
• Flaviu Pop
• Szanto Csaba
• Virgilius-Aurelian Minuță

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.

1. SCIENTIFIC OBJECTIVES:

   1. Contributions to silting theory. The main topics will be the following:
      1. Silting and cosilting complexes in the derived categories. Structures related to these mathematical objects.
      2. The transfer of the (co)silting properties via functors.
   2. Special classes and objects. The topics are the following:
      1. Approximations and definable classes. We will study preenveloping and precovering classes induced by (co)silting objects.
      2. Pure-injective objects in Grothendieck and triangulated categories. We will try to use some triangulated versions for the classical notion of p-functor in order to obtain new information about the class of pure-injective objects.

2. ADMINISTRATIVE OBJECTIVES:

   1. Completion of the research infrastructure by assuring the bibliographical background (books, journals) and the material background of the research (computers, office consumables etc.)
   2. Improving the level of knowledge of the team members and other young researchers and students.

3. RESEARCH SEMINARS:

    (S1) Silting objects in module theory (silting, cosilting and t-tilting 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:

1. Papers submmited or accepted for publication:

   1. S. Breaz: On a theorem of Stelzer for some classes of mixed groups; Mediterr. J. Math., 19 (4) paper no. 159 (2022), 14 pp.
   2. S. Breaz, T. Brzeziński, B. Rybołowicz, P. Saracco: Heaps of modules and affine spaces; arXiv
   3. S. Breaz, Y. Zhou: When is every non central-unit a sum of two nilpotents?; to appear in Contemporary Math.; arXiv
   4. Cs. Szanto, I. Szollosi: Ringel-Hall polynomials associated to a quiver of type $\tilde D_4$
   5. S. Breaz, M. Hrbek, C.-G. Modoi: Silting, cosilting, and extensions of commutative ring; arXiv
   6. S. Breaz, A. Marcus, C.-G. Modoi: Support τ-tilting modules and semibricks over group graded algebras arXiv
   7. Cs. Szanto, I. Szollosi: Ringel-Hall polynomials associated to tame indecomposable modules of defect -2,-1,0,1,2; submitted 2022
   8. S. Breaz, C. Rafiliu: Decompositions of matrices by using commutators; arXiv

2. Preprints:

   1. S. Breaz, C.-G. Modoi: Migration of silting objects via adjoint pairs
   2. S. Breaz, F. Pop: On extriangulated categories

Visits, conferences, workshops

1. 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.
2. 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.
3. Cs. Szanto: Algebra Seminar of Renyi Institute; 07 March 2022; Budapest, Hungary; Talk: Ringel-Hall polynomials associated to a quiver of type $\tilde{D}_{4}$.
4. S. Breaz: Malga Seminar Padova-Verona, Universita di Verona; 24 May 2022; Talk: Silting complexes and extensions of commutative rings.
5. S. Breaz: Functor Categories, Model Theory, and Constructive Category Theory, Universidad de Almeria; 11-15 July 2022; Talk: Change of scalars functors and silting complexes.
6. C.-G. Modoi: Functor Categories, Model Theory, and Constructive Category Theory, Universidad de Almeria; 11-15 July 2022; Talk: Not necessarily compact approximability via silting theory.
7. S. Breaz: Hopf algebras, monoidal categories and related topics; 27-29 July 2022; IMAR, Bucharest, Romania; Talk: Heaps of Modules.
8. A. Marcus: Hopf algebras, monoidal categories and related topics; 27-29 July 2022; IMAR, Bucharest, Romania; Talk: Tilting complexes over a G-graded G-algebra.
9. T. Micu: Young Researchers' Conference on Non-Archimedean and Tropical Geometry; 01-05 August 2022; Universität Regensburg; Talk: The structure of special fibers through valuations.
10. T. Micu: Representation Theory and Triangulated Categories; 26-30 September 2022; Paderborn, Germany.
11. V.-A. Minuță: Representation Theory and Triangulated Categories; 26-30 September 2022; Paderborn, Germany.
12. C.-G. Modoi: Representation Theory and Triangulated Categories; 26-30 September 2022; Paderborn, Germany.
13. S. Breaz: Algebra Seminar of Charles University; 10-12 October 2022; Prague, The Czech Republic; Talk: The Baer-Kaplansky Theorem and Heaps of Modules.

Contact

e-mail:

username: bodo	server: math.ubbcluj.ro
username: ssbreaz	server: gmail.com

fax:
    +40 264 691906
adresa:
    Simion Breaz
    "Babeș-Bolyai" University
    Faculty of Mathematics and Computer Science
    Str. Mihail Kogălniceanu nr. 1
    RO-400084 Cluj-Napoca
    Romania