Project description DEENESFRITPL Study explores the interplay between group theory, operator algebras and topological dynamics Funded by the Marie Skłodowska-Curie Actions programme, GOADS is an interdisciplinary project that aims to study the interplay between group theory, operator algebras and topological dynamics. The project will first focus on a class of C-star algebras associated with algebraic semigroup actions, including example classes stemming from group subshifts of finite type, modules over polynomial rings, rings of algebraic integers and algebraic groups over number fields. Research will also be geared towards the topological full groups associated with algebraic semigroup actions. Show the project objective Hide the project objective 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. Fields of science natural sciencesmathematicspure mathematicsalgebranatural sciencesmathematicspure mathematicsmathematical analysisfunctional analysisoperator algebra Programme(s) H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions Main Programme H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility Topic(s) MSCA-IF-2020 - Individual Fellowships Call for proposal H2020-MSCA-IF-2020 See other projects for this call Funding Scheme MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF) Coordinator UNIVERSITY OF GLASGOW Net EU contribution € 212 933,76 Address UNIVERSITY AVENUE G12 8QQ Glasgow United Kingdom See on map Region Scotland West Central Scotland Glasgow City Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 212 933,76
