Basic Research Project J1-3003
Groups, posets, and complexes

 

Project Title: Groups, posets, and complexes

PI: Russ Woodroofe

Project Code: J1-3003

Type of the Project: basic research project.

Funding Organization: Slovenian Research Agency (ARRS).

Research Field (ARRS): 1.01.00 - Natural Sciences and Mathematics / Mathematics.

Duration: 1. 10. 2021 - 30. 9. 2024.

Project Category: B.

Yearly Range: 1.57 FTE (2.667 research hours).

Sicris profile of the project is avaliable here.

Research Organizations:
University of Primorska, Andrej Marušič Institute.

Project Members:

Chiarelli Nina (ARRS code: 35452)

Dobson Edward Tauscher (ARRS code: 34109)

Fernandez Blas (ARRS code: 52892)

Filipovski Slobodan (ARRS code: 37715)

Krnc Matjaž (ARRS code: 34562)

Miklavič Štefko (ARRS code: 21656)

Milanič Martin (ARRS code: 30211)

Morgan Luke (ARRS code: 52908)

Woodroofe Russ (leader) (ARRS code: 50355)

Abstract:

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 group. The PI and his co-authors 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 classification-dependent 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.