Grupe, poseti, in kompleksi / Groups, posets, and complexes
|
Naziv Tittle |
Grupe, poseti, in kompleksi / Groups, posets, and complexes |
|
Akronim Acronim |
J1-3003 |
|
Opis Description |
(SI) V okviru projekta bomo raziskovali področje na preseku topologije, algebre in kombinatorike. Motivacija za glavne teme projekta so delno urejene množice in simplicialni kompleksi, ki jih srečamo v teoriji grup. Ena od tem se dotika "univerzalne G-geometrije" delno urejene množice odsekov končne grupe. Vodja projekta s soavtorji predlaga nadaljnje delo na osnovi njihovih rezultatov o topologiji te delno urejene množice. S tem povezane tehnike bodo osvetlile posplošene probleme presekov množic. Nadaljnji cilj je dokaz, da mreže podgrup nekomutativnih končnih enostavnih grup niso zaporedno Cohen-Macaulayeve (ta dokaz bo minimalno odvisen od klasifikacije končnih enostavnih grup). S tem bi dobili novo karakterizacijo rešljivih grup, ki je močno neodvisna od obstoječe. S pomočjo te nove karakterizacije bo verjetno omogočila razvoj novih, boljših tehnik za razločevanje kompleksov, ki so zaporedno Cohen-Macaulayevi in tistih, ki niso. (EN) The project will study problems at the intersection of topology, algebra, and combinatorics. The main themes of the project are motivated by posets and simplicial complexes arising in group theory. One theme concerns the "universal G-geometry" of the coset poset of a finite groupe, The PI and his coauthors propose to further their results on the topology of this poset. Related techniques, with a more algebraic geometry flavor, will shed new light on generalized set intersection problems. Another main goal is a minimally classificationdependent proof that the subgroup lattices of nonabelian finite simple groups are not sequentially Cohen-Macaulay. This would make effective a new characterization of solvable groups, highly orthogonal to existing characterizations, and likely would yield better techniques for demarcating between complexes that are sequentially Cohen-Macaulay and those that are not. |
|
Vrsta projekta Project Type |
Temeljni projekt |
|
Trajanje Duration |
01/10/2021 - 30/09/2025 |
|
URL URL |
https://www.upr.si/si/univerza-in-okolje/projekti-univerze-na-primorskem/arrs/567-raziskovalni-projekti/grupe-poseti-in-kompleksi |
|
Vodja projekta Project Leader |
Russell Stephen Woodroofe |
|
Sodelujoče organizacije Participating organizations |
/ |
|
Oddelek Department |
Oddelek za matematiko IAM |