Topološka in algebraična kombinatorika / Topological and Algebraic Combinatorics
|
Naziv Tittle |
Topološka in algebraična kombinatorika / Topological and Algebraic Combinatorics |
|
Akronim Acronim |
N1-0160 |
|
Opis Description |
(SI) Projekt TAC (Topološka in algebraična kombinatorika) bo proučeval probleme na presečišču topologije, algebre in kombinatorike. Obstajata dve glavni temi, obe motivirani z delno urejenimi množicami in simplicialnimi kompleksi, ki se pojavljajo v teoriji grup. Prva tema se nanaša
na topologijo in kombinatoriko mrež odsekov končnih grup.Ta vprašanja so tesno povezana z vprašanji o generiranju in invariantnem generiranju grup ter se povezujejo z velikim številom na videz nepovezanih polj. Druga tema je povezana z Cohen-Macaulayjevimi simplicialnimi kompleksi, zlasti tistimi, ki izhajajo iz algebričnih objektov. Eden glavnih ciljev je poenoten in kar se da od klasifikacije neodvisen dokaz, da podgrupe mrež neabelskih končnih grup niso zaporedno Cohen-Macaulayeve. Napredek pri teh problemih bo verjetno prinesel izboljšane tehnike za razločevanje kompleksov, ki so zaporedno Cohen-Macaulayevi, in tistih, ki niso, saj so koristni drugje znotraj področij algebre in kombinatorike. (EN) The TAC (Topological and Algebraic Combinatorics) project will study problems at the intersection of topology, algebra, and combinatorics. There are two main themes, both motivated by posets and simplicial complexes arising in group theory. The first theme concerns the topology and combinatorics of the lattice of cosets of a finite group. These questions are intimately related to questions about generation and invariable generation of groups, and connect with a large number of seemingly unconnected fields. The second theme is loosely around shellable and sequentially Cohen-Macaulay simplicial complexes, particularly those arising from algebraic objects. One main goal is a unified and minimally classification-dependent proof that the subgroup lattices of nonabelian finite simple groups are not sequentially Cohen-Macaulay. Progress on these problems is likely to yield better techniques for demarcating between complexes that are sequentially Cohen-Macaulay and those that are not, as will be useful elsewhere in algebra and combinatorics. |
|
Vrsta projekta Project Type |
Temeljni projekt |
|
Trajanje Duration |
01/08/2020 - 31/07/2023 |
|
URL URL |
https://p1-0285.iam.upr.si/sl/projekti/n1-160 |
|
Vodja projekta Project Leader |
dr. Russell Stephen Woodrofe |
|
Sodelujoče organizacije Participating organizations |
/ |
|
Oddelek Department |
Oddelek za matematiko IAM |