Customized Project N1-0160
Topological and Algebraic Combinatorics

 

Project Title: Topological and Algebraic Combinatorics

PI: Russ Woodroofe

Project Code: N1-0160.

Type of the Project: customized project.

Funding Organization: Slovenian Research Agency (ARRS).

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

Duration: 1. 8. 2020 - 31. 7. 2023.

Project Category: B.

Yearly Range: 1.60 FTE (2.725 research hours).

Sicris profile of the project is here.

Research Organization: University of Primorska, Andrej Marušič Institute.

Project Members:

• Dobson Edward Tauscher (ARRS code: 3410)
• Woodroofe Russell Stephen (leader, ARRS code: 50355)
• Milanič Martin (ARRS code: 30211)
• Matjaž Krnc (ARRS code: 34562)
• Morgan Luke (ARRS code: 52908)

Abstract:

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.