Department of Mathematics, Faculty of Mathematics and Computer Science, "Babeș-Bolyai" University, Cluj-Napoca

Research Project: "Silting Objects and Approximations"

(Versiune în Română)


Code: PN-IV-P1-PCE-2023-0060
Contract: 92PCE/01.07.2025
Period: July 2025-June 2028
Financed by: Unitatea Executivă pentru Finanțarea Învățământului Superior, a Cercetării, Dezvoltării și Inovării UEFISCDI



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


Team:



Abstract:

The main aim is to study approximations induced by (co)silting objects in various categories. We also study various algebraic invariants in the context of approximation theory.

  1. SCIENTIFIC OBJECTIVES:

    1. Approximations induced by special objects in abstract categories
      1. Approximations in extriangulated categories
      2. t-structures and silting theory in tt-categories
      3. Heaps of modules and trusses
    2. Connections between (silting) approximations and special invariants
      1. Endomorphism rings
      2. Invariants of blocks of normal subgroups
      3. Invariants in the context of approximation theories

  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 various categories (silting, cosilting and τ-tilting modules)
       	(S2) Special categories (extriangulated and tensor triangulated categories, categories of heaps)
        	(S3) G-categories, G-graded categories, and coverings.
        	(S4) Approximations and invariants.

Summary of our activities in the year (Reports): 2025 , 2026 2027 2028



Results:

  1. Papers submmited or accepted for publication:

    1. S. Breaz: On the Waring Problem for Matrices over Finite Fields; Journal ..., volume ... ; arXiv

  2. Preprints:



Visits, conferences, workshops



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