New Geometry of Quantum Dynamics

Projektinformationen

QUANTUM DYNAMICS

ID Finanzhilfevereinbarung: 691246

DOI

10.3030/691246

Projekt abgeschlossen

EK-Unterschriftsdatum 7 Dezember 2015

Startdatum 1 Januar 2016

Enddatum 31 Dezember 2019

Finanziert unter

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Gesamtkosten

€ 589 500,00

EU-Beitrag

€ 288 000,00

Koordiniert durch

INSTYTUT MATEMATYCZNY POLSKIEJ AKADEMII NAUK
Poland

Periodic Reporting for period 2 - QUANTUM DYNAMICS (New Geometry of Quantum Dynamics)

Berichtszeitraum: 2018-01-01 bis 2019-12-31

Zusammenfassung vom Kontext und den Gesamtzielen des Projekts

The main objectives of the project concern the classification, symmetry, structure and noncommutative metric geometry of quantum spaces. The innovation in our approach comes from our combination of ideas from many fields of research such as: operator theory, metric topology and differential geometry, classification theory of C*-algebras, path algebras and Hopf algebras.

All of the aforementioned main objectives have been successfully implemented to the satisfactory extent. A detailed description of our research progress sectioned into five work packages is provided below. The interplay between our scientifically adjacent but distinct work packages yielded innovative and original ideas, as expected. For instance, new equivariant dimensions introduced within WP 1 were applied in computations in WP 3.

Arbeit, die ab Beginn des Projekts bis zum Ende des durch den Bericht erfassten Berichtszeitraums geleistet wurde, und die wichtigsten bis dahin erzielten Ergebnisse

"1. EU-funded secondments: 64 person-months.

2. Other exchange visits between nodes: over 50 person-months.

3. Events: 5

- Conference at the Fields Institute entitled ""Geometry, Representation Theory and the Baum-Connes Conjecture"" (July 18 - 22, 2016)
- Simons Semester at the Banach Center entitled ""Noncommutative geometry the next generation"" (September - November 2016)
- Conference at the Banach Center ""New Geometry of Quantum Dynamics"" (January 15-19, 2018)
- Conference at the Fields Institute entitled ""Workshop on New Geometry of Quantum Dynamics"" (August 12 - 16, 2019)
- Conference at the Banach Center entitled ""The Frontier of Quantum Dynamics"" (December 9 - 13, 2019)

4. Talks (excluding talks at the above meetings): 151

5. Research papers: 72"

Fortschritte, die über den aktuellen Stand der Technik hinausgehen und voraussichtliche potenzielle Auswirkungen (einschließlich der bis dato erzielten sozioökonomischen Auswirkungen und weiter gefassten gesellschaftlichen Auswirkungen des Projekts)

Work Package 1
Title: Noncommutative Borsuk-Ulam-type conjectures
Number of papers (including one PhD thesis): 10

Work Package 2
Title: Noncommutative bordism of quantum fibrations
Number of papers: 12

Work Package 3
Title: Trimming and growing of graphs for graph algebras
Number of papers: 21

Work Package 4
Title: Noncommutative metric geometry of C*-dynamical systems and graph C*-algebras
Number of papers: 16

Work Package 5
Title: Noncommutative spectral geometry for quantum group homogeneous spaces
Number of papers: 20

This gives the total of 79 research papers.

poster2-1.jpg

poster1-1.jpg

poster3-1.jpg