Departamentul de Matematică, Facultatea de Matematică și Informatică, Universitatea "Babeș-Bolyai", Cluj-Napoca

Proiect de cercetare: "Contribuții la Teoria Silting"

(English version)


Cod: PN-III-P4-ID-PCE-2020-0454
Contract: 75/04.01.2021
Perioada: Ianuarie 2021-Decembrie 2023
Finanțat de: Unitatea Executivă pentru Finanțarea Învățământului Superior, a Cercetării, Dezvoltării și Inovării UEFISCDI



  1. Echipa
  2. Rezumatul proiectului
  3. Rezultate
  4. Vizite de cercetare, conferințe, workshop-uri
  5. Contact


Echipa:



Rezumatul proiectului:

Scopul acestui proiect este studiul obiectelor (co)silting care pot fi asociate unor categorii (e.g., de module, Grothendieck sau triangulate).

  1. OBIECTIVE ȘTIINȚIFICE:

    1. Contribuții la teoria silting. Subiectele principale vor fi următoarele:
      1. Complexe silting și cosilting în categorii derivate. Structuri legate de aceste obiecte matematice.
      2. Transferul proprietăților (co)silting via functori.
    2. Clase speciale și obiecte speciale. Subiectele vor fi următoarele:
      1. Aproximări și clase definite. Vom studia clasele pre-înfășurătoare și pre-acoperitoare induse de obiecte (co)silting.
      2. Obiecte pur-injective în categorii Grothendieck și categorii triangulate. Vom încerca să utilizăm versiuni categoriale ale noțiunii clasice de p-functor, pentru a obține informații noi despre clasa obiectelor pur-injective.

  2. OBIECTIVE ADMINISTRATIVE:

    1. Completarea infrastrucurii de cercetare prin asigurarea resurselor bibliografice (cărți, jurnale) și a instrumentarului necesar cercetării (calculatoare, consumabile de birou, etc.).
    2. Îmbunătățirea nivelului cunoștințelor membrilor echipei și a altor tineri cercetători sau studenți.

  3. ACTIVITĂȚI (SEMINARII DE CERCETARE):

       (S1) Obiecte silting în teoria modulelor (module silting, cosilting și τ-tilting) 
       (S2) Obiecte silting în teoria categoriilor 
       (S3) Proprietăți de scindare și structura modulelor (pur) proiective și (pur) injective
       (S4) Identități în inele și aproximări

Rezumatul activităților din anul: 2021 , 2022 , 2021-2023 , 2021-2023 (in engleza)



Rezultate:


Sumar: Rezultatele obtinute se refera la mai multe contexte: teoria generala a obictelor silting in categorii triangulate, dar si situatii particulare (categorii derivate peste inele comutative sau dg-algebre, respectiv teoria $\tau$-tilting pentru generalizari ale algebrelor grupale) care necesita, fiecare in parte, abordari si tehnici speciale. De asemenea, din investigatiile facute de membrii echipei s-au obtinut rezultate despre categorii de module peste algebre finit dimensionale (grupale sau de drumuri peste tolbe speciale) sau despre metode de a asocia structuri afine categoriilor de module.

  1. Conferinta: Trends in Representation Theory and Related Topics

  2. Articole trimise spre publicare sau acceptate spre publicare:

    1. S. Breaz: A characterization of (co)silting objects, arXiv
    2. S. Breaz, G.C. Modoi: Derived equivalences induced by good silting complexes, in Functor Categories, Model Theory, Algebraic Analysis and Constructive Methods, editor Alexander Martsinkovsky, book series Springer Proceedings in Mathematics and Statistics
    3. A. Marcus, V.A. Minuta: An exact sequence for the graded Picent, Journal of Group Theory, arXiv
    4. I. Simion, D. Testerman: On minimal epimorphic subgroups in simple algebraic groups of rank 2, arXiv
    5. S. Breaz, T. Brzeziński, B. Rybołowicz, P. Saracco: Heaps of modules: Categorical aspects, arXiv
    6. S. Breaz, M. Hrbek, G.C. Modoi: Silting, cosilting, and extensions of commutative rings, arXiv
    7. S. Breaz, A. Marcus, C.-G. Modoi: Support τ-tilting modules and semibricks over group graded algebras, J. Algebra 637 (2024), 90--111 arXiv
    8. S. Breaz, T. Brzeziński, B. Rybołowicz, P. Saracco: Heaps of modules and affine spaces; Annali di Matematica Pura ed Applicata (1923--). https://doi.org/10.1007/s10231-023-01369-0 (2023) arXiv
    9. S. Breaz, C. Rafiliu: Decompositions of matrices by using commutators; Linear Algebra and its Applications, 662 (2023), 39--48; arXiv
    10. Cs. Szanto, I. Szollosi: On some Ringel-Hall polynomials associated to tame indecomposable modules, Journal of Pure and Applied Algebra<\i>, paper
    11. S. Breaz: On a theorem of Stelzer for some classes of mixed groups; Mediterr. J. Math., 19 (4) nr. articol 159 (2022), 14 pagini
    12. Cs. Szanto, I. Szollosi: Ringel-Hall polynomials associated to a quiver of type $\tilde D_4$, Period Math Hung (2023), paper
    13. S. Breaz, Y. Zhou: When is every non central-unit a sum of two nilpotents?; va apărea în Contemporary Math. 785 (2023), 47--55. arXiv
    14. Cs. Szanto, I. Szollosi: Combinatorial methods in the representation theory of finite dimensional tame algebras, monografie 2023.


  3. Vizite de cercetare, conferințe, workshop-uri

    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.
    14. S. Breaz: The Tenth Congress of Romanian Mathematicians, June 30-July 5, 2023, Pitesti, Romania; Talk: Change of scalars and bounded silting complexes.
    15. G.C. Modoi: The Tenth Congress of Romanian Mathematicians, June 30-July 5, 2023, Pitesti, Romania; Talk: Migration of silting-like properties via adjoint pairs.
    16. V.-A. Minuta: The Tenth Congress of Romanian Mathematicians, June 30-July 5, 2023, Pitesti, Romania; Talk: An exact sequence for the graded Picent group.
    17. I.I. Simion: The Tenth Congress of Romanian Mathematicians, June 30-July 5, 2023, Pitesti, Romania; Talk: On the product expansion of normal subsets in simple groups.
    18. S. Breaz: Trends in Representation Theory and Related Topics, 12-16 Septembrie 2023, Babe\c s-Bolyai University Cluj-Napoca, Romania, \url{https://math.ubbcluj.ro/trtrt2023}. Talk: On a characterization of (co)silting objects.
    19. Cs. Szanto: Summer school, Quiver Representations, Quiver Varieties and Combinatorics (BIP Blended Intensive Program), 22-26 Mai 2023, Bologna University, Italia, \url{https://eventi.unibo.it/bip-quiver/summer-school}. Talk: Ringel-Hall polynomials associated to tame quivers.
    20. Cs. Szanto: Trends in Representation Theory and Related Topics, 12-16 Septembrie 2023, Babe\c s-Bolyai University Cluj-Napoca, Romania, \url{https://math.ubbcluj.ro/trtrt2023}. Talk: Ringel-Hall polynomials associated to tame quivers.
    21. A. Marcus: 17th International Conference on Applied Mathematics and Computer Science, 11-13 Iulie 2023, Technical University Cluj-Napoca. Talk: Support tau-tilting modules and semibricks over group graded algebras.
    22. V.-A. Minuta: 17th International Conference on Applied Mathematics and Computer Science, 11-13 July 2023, Cluj-Napoca, Romania. Talk: An exact sequence for the graded Picent group
    23. I.-I. Simion: Trends in Representation Theory and Related Topics, September 12-16, 2023, Cluj-Napoca, Romania, \url{https://math.ubbcluj.ro/trtrt2023}. Talk: Epimorphic subgroups in simple algebraic groups.
    24. V.-A. Minuta: Trends in Representation Theory and Related Topics, 12-16 September 2023, Cluj-Napoca, Romania, \url{https://math.ubbcluj.ro/trtrt2023}. Talk: Relations between module triples, and derived equivalences for wreath products
    25. S. Breaz: Homological Algebra and Representation Theory, 10-14 July 2023, Karlovasi, Samos, Greece.
    26. G. C. Modoi: Homological Algebra and Representation Theory, 10-14 July 2023, Karlovasi, Samos, Greece.
    27. G. C. Modoi: Trends in Representation Theory and Related Topics, 12-16 Septembrie 2023, Babe\c s-Bolyai University Cluj-Napoca.
    28. A. Marcus: The 10-th Congress of Romanian Mathematicians, 30.06-05.07 2023, Pitesti, Romania.
    29. A. Marcus: Trends in Representation Theory and Related Topics, 12-16 Septembrie 2023, Babe\c s-Bolyai University Cluj-Napoca.
    30. T. Micu: Trends in Representation Theory and Related Topics, 12-16 Septembrie 2023, Babe\c s-Bolyai University Cluj-Napoca.
    31. C. Pelea: Trends in Representation Theory and Related Topics, 12-16 Septembrie 2023, Babe\c s-Bolyai University Cluj-Napoca.
    32. T. Micu: - Summer School on Higher Structures in Algebra and Geometry; 13-18 August 2023; Nordfjordeid, Norway.
    33. T. Micu: Tau-Tilting Research School; 5-8 September 2023; Koln, Germany.
    34. T. Micu: Representation Theory and Triangulated Categories; 26-30 September 2022; Paderborn, Germany.
    35. V.-A. Minuta: Representation Theory and Triangulated Categories; 26-30 September 2022; Paderborn, Germany.


    Contact

    e-mail:
    nume de utilizator: bodo    server: math.ubbcluj.ro
    nume de utilizator: ssbreaz    server: gmail.com
    fax:
        +40 264 691906
    adresa:
        Simion Breaz
        Universitatea "Babeș-Bolyai"
        Facultatea de Matematică și Informatică
        Str. Mihail Kogălniceanu nr. 1
        RO-400084 Cluj-Napoca
        România