GOADS · Groups, operator algebras, and dynamics
Horizon 2020 — Marie Skłodowska-Curie Actions
- Duration
- 2022-05-01 → 2024-04-30
- EU contribution
- €212,934
- Participants
- 1
- Scheme
- MSCA-IF
Lines connect the coordinator with its partners.
Results in brief
Groups, operator algebras, and dynamics
The project lies at the intersection of operator algebras, (semi)group theory, and topological dynamics. We initiated a systematic study of C*-algebras and groupoids attached to algebraic actions of semigroups, with applications to group theory. Such actions are the “irreversible’’ analogues of the well-studied algebraic actions of groups. The project aim comprised two objectives: Objective A was concerned with the structure of the canonical concrete C*-algebras associated with algebraic actions; Objective B was concerned with groupoids associated with algebraic actions and their topological full groups. This MSCA-IF facilitated many collaborations and interactions of the ER with researcher from around the globe, and it helped the ER obtain a permanent academic position.
Data: CORDIS, © European Union
Project objective
The proposed research project fits into the broad programme of studying C*-algebras and groups dynamical origin, and ishighly interdisciplinary in nature; it advances novel interactions among operator algebras, group theory, and topological dynamics. This project has two facets: First, I shall initiate the systematic study of a class of C*-algebras associated with algebraic semigroup actions, including example classes coming from group subshifts of finite type, modules over polynomial rings, rings of algebraic integers, and algebraic groups over number fields. After investigating structural properties of these C*-algebras, including ideal structure, pure infiniteness, Cartans, classifiability, and K-theory, I shall give a careful analysis of the Kubo--Martin--Schwinger (KMS) states for canonical time evolutions on these C*-algebras, and explore a mysterious connection between KMS states and K-theory that has manifested itself in the context of ax+b-semigroups. I will also look for connections between KMS states and entropy of algebraic actions. Second, I shall begin the study of the topological full groups associated with algebraic semigroup actions: I want to establish rigidity results and classify embeddings between these full groups, and I will study group-theoretic properties, including (co)homological finiteness conditions and the Haagerup property. I will then investigate Matui's AH conjecture in this setting, and explore whether non-sofic full groups exist.The project will strengthen my career by giving me the opportunity to work with leading experts in C*-algebras, group theory, and topological dynamics. It will also give me management skills by co-organising an international workshop, it willprovide new possibilities for collaboration, and it will advance my ability as a researcher, so that I can obtain a permanentposition at a research-oriented university. It will also open up new opportunities for collaboration between Glasgow, Lyon, Oslo, and the US.
Original text from CORDIS.
Participants
- UNIVERSITY OF GLASGOW · GlasgowCoordinatorUnited Kingdom
Links
Data: CORDIS, © European Union