Objective Topologically ordered phases are a new state of matter, discovered only around the late '80s. In recent years interest in such states has sparked, one of the reasons being applications to topological quantum computing: the topological properties make the state robust against perturbations, making them ideal components in an environment where (thermal or other) noise is one's biggest enemy. By now there is a plethora of examples of topologically ordered states, whose only unifying feature seems to be that they do not fall into the Landau theory of phases. Although there are many examples, the mathematical framework to rigorously study such systems is less clear, in particular if one wants to consider both so-called long range entangled phases and symmetry protected phases. The goal of this project is to tackle this problem.The approach that is proposed is to use operator algebraic methods to focus on the algebraic properties of the observables in such systems. This approach has proved successful in algebraic quantum field theory. Using this attack the aim is to find tools to classify the different topological phases, and in particular find methods that are applicable a wide class of models, despite looking very different at first sight. These ideas will be tested on the wide range of topological systems that is available. The focus in this project is on stability properties on the one hand, in particular for invariants of topological phases, and the study of boundary theories on the other hand. Fields of science natural sciencesmathematicspure mathematicstopologynatural sciencesphysical sciencesquantum physicsquantum field theoryengineering and technologyelectrical engineering, electronic engineering, information engineeringelectronic engineeringcomputer hardwarequantum computersnatural sciencesmathematicspure mathematicsarithmeticsprime numbers 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-2014-GF - Marie Skłodowska-Curie Individual Fellowships (IF-GF) Call for proposal H2020-MSCA-IF-2014 See other projects for this call Funding Scheme MSCA-IF-GF - Global Fellowships Coordinator RHEINISCH-WESTFAELISCHE TECHNISCHE HOCHSCHULE AACHEN Net EU contribution € 257 860,80 Address TEMPLERGRABEN 55 52062 Aachen Germany See on map Region Nordrhein-Westfalen Köln Städteregion Aachen 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 € 257 860,80 Partners (1) Sort alphabetically Sort by Net EU contribution Expand all Collapse all Partner Partner organisations contribute to the implementation of the action, but do not sign the Grant Agreement. THE REGENTS OF THE UNIVERSITY OF CALIFORNIA United States Net EU contribution € 0,00 Address FRANKLIN STREET 1111 12 FLOOR 94607 OAKLAND CA See on map 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 € 172 130,40
