New Geometry of Quantum Dynamics

Project Information

QUANTUM DYNAMICS

Grant agreement ID: 691246

DOI

10.3030/691246

Project closed

EC signature date 7 December 2015

Start date 1 January 2016

End date 31 December 2019

Funded under

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Total cost

€ 589 500,00

EU contribution

€ 288 000,00

Coordinated by

INSTYTUT MATEMATYCZNY POLSKIEJ AKADEMII NAUK
Poland

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

Reporting period: 2018-01-01 to 2019-12-31

Summary of the context and overall objectives of the project

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.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

"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"

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

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.

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