UNIRI projekt 2024 | UNIRI project 2024

Algebarske strukture i njihove primjene u teoriji brojeva i topologiji

Algebraic structures and their applications in number theory and topology

Algebarske strukture jedan su od osnovnih koncepata u matematici. Predstavljaju temelj algebre, kao grane matematike, ali istovremeno se primjenjuju u brojnim drugim matematičkim granama. U okviru projekta sudionice će se baviti trima različitim temama kojima je zajedničko korištenje algebarskih struktura: teorijom reprezentacija afinih Kac–Moodyjevih Liejevih algebri, Diofantovim m-torkama u prstenima polinoma te u brojevnim prstenima i poljima te aproksimativnim grupama i njihovim grubo-dimenzionalnim svojstvima.

Algebraic structures are among the basic notions in mathematics. They represent the foundation of algebra, as a branch of mathematics, while also being applied in other mathematical subfields. Within this project, the participants will pursue three different subjects, for which using algebraic structures is a common trait: representation theory of affine Kac-Moody Lie algebras, Diophantine m-tuples in polynomial rings and in number rings and fields, approximate groups and their coarse-dimensional properties.

Voditelj / Principal investigator:

izv. prof. dr. sc. Ana Jurasić

e-mail: ajurasic@math.uniri.hr

(Fakultet za matematiku, Sveučilište u Rijeci / Faculty of Mathematics, University of Rijeka)

Istraživački tim / Research team:

izv. prof. dr. sc. Marijana Butorac

(Fakultet za matematiku, Sveučilište u Rijeci / Faculty of Mathematics, University of Rijeka)

doc. dr. sc. Vera Tonić

(Fakultet za matematiku, Sveučilište u Rijeci / Faculty of Mathematics, University of Rijeka)

Objavljeni radovi / Published works:

Tobias Hartnick, Vera Tonić, Hurewicz and Dranishnikov-Smith theorems for asymptotic dimension of countable approximate groups, Topology and its Applications, Volume 349, 15 May 2024, 108905 (16 pages)

Vera Tonić, A Hurewicz-type formula for asymptotic-dimension-lowering symmetric quasimorphisms of countable approximate groups, Rad Hrvatske akademije znanosti i umjetnosti. Razred za matematičke, fizičke i kemijske znanosti. Matematičke znanosti, (2025)

Vera Tonić, Some coarse properties of global morphisms of countable approximate groups, accepted for publication in Acta Mathematica Spalatensia

Pozvana predavanja / Invited talks:

Izlaganja na konferencijama / Talks:

8th Croatian Mathematical Congress, Osijek, Croatia, July 2-5, 2024:

Marijana Butorac, Combinatorial bases of standard modules for twisted affine Lie algebras

Ana Jurasić, On the existence of D(2X+1)-quadruples in Z[X]

Vera Tonić, Hurewicz mapping theorem for asymptotic dimension of countable approximate groups

Članovi istraživačkog tima izlažu o svojim rezultatima i u okviru Research Classa Zavoda za algebru i teoriju brojeva.