New Geometry of Quantum Dynamics

Deliverables

Dissemination: NCG seminar (Trimming and growing of graphs for graph algebras)

D2 seminars and talks are the second tangible deliverable related to scientific output: we shall continuously collect recordings of the NCG Seminar at IMPAN as well as either slides or recordings from other seminars by the members of the team – and summarize them on a yearly basis (M12, M24, M36, M48) to monitor the dissemination. All deliverables of this type shall be available on the Web page and/or youtube channel.

Dissemination: NCG seminar (Noncommutative spectral geometry for quantum group homogeneous spaces)

Focus programme (Noncommutative metric geometry of C*-dynamical systems and graph C*-algebras)

D7 Focus Program at the Fields Insttute – is expected to be the final and summarising event of the project, the deliverable will be talks (recorded and slides)/abstracts of lectures/seminars during the event (in a form of the web page).

Simons Semester at the Banach Center (Noncommutative bordism of quantum fibrations)

D5 Simons Semester at the Banach Center: network-wide event planned at the Banach center, the deliverable will comprise talks (recorded and slides)/abstracts of lectures/ seminars during the event (in a form of the web page).

Proceedings (Trimming and growing of graphs for graph algebras)

D6 Proceedings: Banach Center Proceedings of the planned Simons Semester at IMPAN, Noncommutative geometry the next generation will contain the research papers submitted to the volume.

Special issue (Noncommutative spectral geometry for quantum group homogeneous spaces)

D8 Special issue of SIGMA: Special issue of Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) on New Geometry of Quantum Dynamics will be a closing volume summarising scientific achievements of the project with submitted papers by majority (if not all) participants.

Focus programme (Trimming and growing of graphs for graph algebras)

Special issue (Trimming and growing of graphs for graph algebras)

Research papers (Noncommutative bordism of quantum fibrations)

D1 research papers are the crucial deliverable, which monitors the scientific output of the project and the progress in the realisation of the project as well as the effectiveness of the collaborations. Since papers will be made available irregularly we shall update the information on them continuously, however, to effectively monitor the outcome we shall summarize the publications and collect them on a yearly basis (M12, M24, M36, M48). Deliverable shall be made available and through Arxives/web page.

Simons Semester at the Banach Center (Trimming and growing of graphs for graph algebras)

Special issue (Noncommutative metric geometry of C*-dynamical systems and graph C*-algebras)

Proceedings (Noncommutative bordism of quantum fibrations)

D6 Proceedings: Banach Center Proceedings of the planned Simons Semester at IMPAN, Noncommutative geometry the next generation will contain the research papers submitted to the volume.

Research papers (Noncommutative Borsuk–Ulam-type conjectures)

Focus programme (Noncommutative spectral geometry for quantum group homogeneous spaces)

Research papers (Trimming and growing of graphs for graph algebras)

Dissemination: NCG seminar (Noncommutative metric geometry of C*-dynamical systems and graph C*-algebras)

Proceedings (Noncommutative spectral geometry for quantum group homogeneous spaces)

D6 Proceedings: Banach Center Proceedings of the planned Simons Semester at IMPAN, Noncommutative geometry the next generation will contain the research papers submitted to the volume.

Research papers (Noncommutative metric geometry of C*-dynamical systems and graph C*-algebras)

Simons Semester at the Banach Center (Noncommutative metric geometry of C*-dynamical systems and graph C*-algebras)

Proceedings (Noncommutative metric geometry of C*-dynamical systems and graph C*-algebras)

D6 Proceedings: Banach Center Proceedings of the planned Simons Semester at IMPAN, Noncommutative geometry the next generation will contain the research papers submitted to the volume.

Research papers (Noncommutative spectral geometry for quantum group homogeneous spaces)

Special issue (Noncommutative Borsuk–Ulam-type conjectures)

Focus programme (Noncommutative bordism of quantum fibrations)

Focus programme (Noncommutative Borsuk–Ulam-type conjectures)

Proceedings (Noncommutative Borsuk–Ulam-type conjectures)

D6 Proceedings: Banach Center Proceedings of the planned Simons Semester at IMPAN, Noncommutative geometry the next generation will contain the research papers submitted to the volume.

Dissemination: NCG seminar (Noncommutative Borsuk–Ulam-type conjectures)

Simons Semester at the Banach Center (Noncommutative Borsuk–Ulam-type conjectures)

Special issue (Noncommutative bordism of quantum fibrations)

Dissemination: NCG seminar (Noncommutative bordism of quantum fibrations)

Simons Semester at the Banach Center (Noncommutative spectral geometry for quantum group homogeneous spaces)

D5 Simons Semester at the Banach Center: network-wide event planned at the Banach center, the deliverable will comprise talks (recorded and slides)/abstracts of lectures/seminars during the event (in a form of the web page).

Dedicated Web page (Management)

D3 dedicated Web page shall be created at the beginning of the project and updated on a continuous basis: page will hold all information pertaining to the project: about secondments, dissemination (publications, preprints, talks, seminars) and events which involve and/or are related to the project. The internal section of the web page (which includes internal reports) shall be available to project team.

Progress report (Management)

Progress report will summarize the scientific achievements, secondments, dissemination and commmunication (outreach activities) by the participants. Deliverable shall be archived/stored at IMPAN, electronic vesions shall be available on the Web page.

Progress report 2 (Management)

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Publications

Continuity of spectral radius and type I $C^*$-algebras

Author(s): Tatiana Shulman
Published in: Proceedings of the American Mathematical Society, Issue 147/2, 2019, Page(s) 641-646, ISSN 0002-9939
DOI: 10.1090/proc/14169

Quantum actions on discrete quantum spaces and a generalization of Clifford’s theory of representations

Author(s): Kenny De Commer, Paweł Kasprzak, Adam Skalski, Piotr M. Sołtan
Published in: Israel Journal of Mathematics, Issue 226/1, 2018, Page(s) 475-503, ISSN 0021-2172
DOI: 10.1007/s11856-018-1709-x

I-factorial quantum torsors and Heisenberg algebras of quantized universal enveloping type

Author(s): Kenny De Commer
Published in: Journal of Functional Analysis, Issue 274/1, 2018, Page(s) 152-221, ISSN 0022-1236
DOI: 10.1016/j.jfa.2017.09.005

Partial actions of $C^{*}$ -quantum groups

Author(s): Franziska Kraken, Paula Quast, Thomas Timmermann
Published in: Banach Journal of Mathematical Analysis, Issue 12/4, 2018, Page(s) 843-872, ISSN 1735-8787
DOI: 10.1215/17358787-2017-0056

Ribbon Braided Module Categories, Quantum Symmetric Pairs and Knizhnik–Zamolodchikov Equations

Author(s): Kenny De Commer, Sergey Neshveyev, Lars Tuset, Makoto Yamashita
Published in: Communications in Mathematical Physics, Issue 367/3, 2019, Page(s) 717-769, ISSN 0010-3616
DOI: 10.1007/s00220-019-03317-7

Free products with amalgamation over central $\mathrm {C}^*$-subalgebras

Author(s): Kristin Courtney, Tatiana Shulman
Published in: Proceedings of the American Mathematical Society, Issue 148/2, 2020, Page(s) 765-776, ISSN 0002-9939
DOI: 10.1090/proc/14746

The field of quantum $$GL(N,\pmb {\mathbb {C}})$$ G L ( N , C )

Author(s): Kenny De Commer, Matthias Floré
Published in: Selecta Mathematica, Issue 25/1, 2019, ISSN 1022-1824
DOI: 10.1007/s00029-019-0456-0

Geometric Classification of Graph C*-algebras over Finite Graphs

Author(s): Søren Eilers, Gunnar Restorff, Efren Ruiz, Adam P.W. Sørensen
Published in: Canadian Journal of Mathematics, Issue 70/2, 2018, Page(s) 294-353, ISSN 0008-414X
DOI: 10.4153/cjm-2017-016-7

A dynamical characterization of diagonal-preserving -isomorphisms of graph -algebras

Author(s): SARA E. ARKLINT, SØREN EILERS, EFREN RUIZ
Published in: Ergodic Theory and Dynamical Systems, Issue 38/7, 2018, Page(s) 2401-2421, ISSN 0143-3857
DOI: 10.1017/etds.2016.141

Projective Modules Over Quantum Projective Line

Author(s): Albert Jeu-Liang Sheu
Published in: International Journal of Mathematics, Issue 28/03, 2017, Page(s) 1750022, ISSN 0129-167X
DOI: 10.1142/s0129167x17500227

Representations of higher-rank graph C⁎-algebras associated to Λ-semibranching function systems

Author(s): Carla Farsi, Elizabeth Gillaspy, Palle Jorgensen, Sooran Kang, Judith Packer
Published in: Journal of Mathematical Analysis and Applications, Issue 468/2, 2018, Page(s) 766-798, ISSN 0022-247X
DOI: 10.1016/j.jmaa.2018.08.051

Projections over quantum homogeneous odd-dimensional spheres

Author(s): Albert Jeu-Liang Sheu
Published in: Journal of Functional Analysis, Issue 277/10, 2019, Page(s) 3491-3512, ISSN 0022-1236
DOI: 10.1016/j.jfa.2019.05.006

Noncommutative solenoids and the Gromov-Hausdorff propinquity

Author(s): Frédéric Latrémolière, Judith Packer
Published in: Proceedings of the American Mathematical Society, Issue 145/5, 2017, Page(s) 2043-2057, ISSN 0002-9939
DOI: 10.1090/proc/13229

Equivalence of quantum metrics with a common domain

Author(s): Frédéric Latrémolière
Published in: Journal of Mathematical Analysis and Applications, Issue 443/2, 2016, Page(s) 1179-1195, ISSN 0022-247X
DOI: 10.1016/j.jmaa.2016.05.045

Vector bundles for “Matrix algebras converge to the sphere”

Author(s): Marc A. Rieffel
Published in: Journal of Geometry and Physics, Issue 132, 2018, Page(s) 181-204, ISSN 0393-0440
DOI: 10.1016/j.geomphys.2018.06.003

The Podleś sphere as a spectral metric space

Author(s): Konrad Aguilar, Jens Kaad
Published in: Journal of Geometry and Physics, Issue 133, 2018, Page(s) 260-278, ISSN 0393-0440
DOI: 10.1016/j.geomphys.2018.07.015

Convergence of Cauchy sequences for the covariant Gromov–Hausdorff propinquity

Author(s): Frédéric Latrémolière
Published in: Journal of Mathematical Analysis and Applications, Issue 469/1, 2019, Page(s) 378-404, ISSN 0022-247X
DOI: 10.1016/j.jmaa.2018.09.018

The Standard Model in noncommutative geometry: fundamental fermions as internal forms

Author(s): Ludwik Dąbrowski, Francesco D’Andrea, Andrzej Sitarz
Published in: Letters in Mathematical Physics, Issue 108/5, 2018, Page(s) 1323-1340, ISSN 0377-9017
DOI: 10.1007/s11005-017-1036-x

Gauss-Bonnet for matrix conformally rescaled Dirac

Author(s): Masoud Khalkhali, Andrzej Sitarz
Published in: Journal of Mathematical Physics, Issue 59/6, 2018, Page(s) 063505, ISSN 0022-2488
DOI: 10.1063/1.4997381

Spectral triples on the Jiang-Su algebra

Author(s): Jacopo Bassi, Ludwik Dąbrowski
Published in: Journal of Mathematical Physics, Issue 59/5, 2018, Page(s) 053507, ISSN 0022-2488
DOI: 10.1063/1.5026311

Families of spectral triples and foliations of space(time)

Author(s): Koen van den Dungen
Published in: Journal of Mathematical Physics, Issue 59/6, 2018, Page(s) 063507, ISSN 0022-2488
DOI: 10.1063/1.5021305

K-theory and index pairings for C*-algebras generated by $q$-normal operators

Author(s): Ismael Cohen, Elmar Wagner
Published in: Rocky Mountain Journal of Mathematics, Issue 48/5, 2018, Page(s) 1485-1510, ISSN 0035-7596
DOI: 10.1216/rmj-2018-48-5-1485

Fermion masses, mass-mixing and the almost commutative geometry of the Standard Model

Author(s): Ludwik Dąbrowski, Andrzej Sitarz
Published in: Journal of High Energy Physics, Issue 2019/2, 2019, ISSN 1029-8479
DOI: 10.1007/jhep02(2019)068

Quantum flag manifolds, quantum symmetric spaces and their associated universal K-matrices

Author(s): K. De Commer, M. Matassa
Published in: Advances in Mathematics, Issue 366, 2020, Page(s) 107029, ISSN 0001-8708
DOI: 10.1016/j.aim.2020.107029

Triviality of equivariant maps in crossed products and matrix algebras

Author(s): Benjamin W Passer
Published in: The Quarterly Journal of Mathematics, Issue 70/1, 2018, Page(s) 289-303, ISSN 0033-5606
DOI: 10.1093/qmath/hay044

Representations of quantum SU(2) operators on a local chart

Author(s): Elmar Wagner
Published in: Journal of Physics: Conference Series, Issue 670, 2016, Page(s) 012053, ISSN 1742-6588
DOI: 10.1088/1742-6596/670/1/012053

Integrable lifts for transitive Lie algebroids

Author(s): Iakovos Androulidakis, Paolo Antonini
Published in: International Journal of Mathematics, Issue 29/09, 2018, Page(s) 1850062, ISSN 0129-167X
DOI: 10.1142/S0129167X18500623

Noncommutative Borsuk-Ulam-type conjectures

Author(s): Paul F. Baum, Ludwik Dąbrowski, Piotr M. Hajac
Published in: Banach Center Publications, Issue 106, 2015, Page(s) 9-18, ISSN 0137-6934
DOI: 10.4064/bc106-0-1

Variations of projectivity for C∗-algebras

Author(s): Don Hadwin, Tatiana Shulman
Published in: Pacific Journal of Mathematics, Issue 301/2, 2019, Page(s) 421-440, ISSN 0030-8730
DOI: 10.2140/pjm.2019.301.421

The index of generalised Dirac–Schrödinger operators

Author(s): Koen van den Dungen
Published in: Journal of Spectral Theory, Issue 9/4, 2019, Page(s) 1459-1506, ISSN 1664-039X
DOI: 10.4171/JST/283

A Correspondence Between Homogeneous and Galois Coactions of Hopf Algebras

Author(s): Kenny De Commer, Johan Konings
Published in: Algebras and Representation Theory, 2020, ISSN 1386-923X
DOI: 10.1007/s10468-019-09892-6

The modular Gromov–Hausdorff propinquity

Author(s): Frédéric Latrémolière
Published in: Dissertationes Mathematicae, Issue 544, 2019, Page(s) 1-70, ISSN 0012-3862
DOI: 10.4064/dm778-5-2019

The covariant Gromov–Hausdorff propinquity

Author(s): Frédéric Latrémolière
Published in: Studia Mathematica, Issue 251/2, 2020, Page(s) 135-169, ISSN 0039-3223
DOI: 10.4064/sm180610-28-12

Monic representations of finite higher-rank graphs

Author(s): CARLA FARSI, ELIZABETH GILLASPY, PALLE JORGENSEN, SOORAN KANG, JUDITH PACKER
Published in: Ergodic Theory and Dynamical Systems, Issue 40/5, 2020, Page(s) 1238-1267, ISSN 0143-3857
DOI: 10.1017/etds.2018.79

Actions of categories by Lipschitz morphisms on limits for the Gromov–Hausdorff propinquity

Author(s): Frédéric Latrémolière
Published in: Journal of Geometry and Physics, Issue 146, 2019, Page(s) 103481, ISSN 0393-0440
DOI: 10.1016/j.geomphys.2019.103481

Spin geometry of the rational noncommutative torus

Author(s): Alessandro Carotenuto, Ludwik Dąbrowski
Published in: Journal of Geometry and Physics, Issue 144, 2019, Page(s) 28-42, ISSN 0393-0440
DOI: 10.1016/j.geomphys.2019.05.008

Model theory and Rokhlin dimension for compact quantum group actions

Author(s): Eusebio Gardella, Mehrdad Kalantar, Martino Lupini
Published in: Journal of Noncommutative Geometry, Issue 13/2, 2019, Page(s) 711-767, ISSN 1661-6952
DOI: 10.4171/jncg/337

Compact group actions on topological and noncommutative joins

Author(s): Alexandru Chirvasitu, Benjamin Passer
Published in: Proceedings of the American Mathematical Society, Issue 146/8, 2018, Page(s) 3217-3232, ISSN 0002-9939
DOI: 10.1090/proc/13941

Dirac operator and its cohomology for the quantum group Uq()

Author(s): Pavle Pandžić, Petr Somberg
Published in: Journal of Mathematical Physics, Issue 58/4, 2017, Page(s) 041702, ISSN 0022-2488
DOI: 10.1063/1.4979623

Convergence of Quotients of AF Algebras in Quantum Propinquity by Convergence of Ideals

Author(s): Konrad Aguilar
Published in: Journal of Operator Theory, 2019, ISSN 0379-4024
DOI: 10.7900/jot.2018jun13.2222

Cuntz Semigroups of Compact-Type Hopf C*-Algebras

Author(s): Dan Kučerovský
Published in: Axioms, Issue 6/4, 2017, Page(s) 1, ISSN 2075-1680
DOI: 10.3390/axioms6010001

Cotangent bundles for “matrix algebras converge to the sphere”

Author(s): Marc A. Rieffel
Published in: Expositiones Mathematicae, 2020, ISSN 0723-0869
DOI: 10.1016/j.exmath.2020.01.006

Filtered K-theory for graph algebras

Author(s): Søren Eilers, Gunnar Restorff, Efren Ruiz, Adam P.W. Sørensen
Published in: MATRIX Book Series, Issue 1, 2018, Page(s) 229–249

On Noncommutative Geometry of the Standard Model: Fermion Multiplet as Internal Forms

Author(s): Ludwik Dąbrowski
Published in: Geometric Methods in Physics XXXVI, 2017

Dirac Operator on a Noncommutative Toeplitz Torus

Author(s): Fredy Díaz García, Elmar Wagner
Published in: Geometric Methods in Physics XXXVI - Workshop and Summer School, Białowieża, Poland, 2017, 2019, Page(s) 103-109
DOI: 10.1007/978-3-030-01156-7_11

Associated noncommutative vector bundles over the Vaksman-Soibelman quantum complex projective spaces

Author(s): Francesca Arici, Piotr M. Hajac, Mariusz Tobolski
Published in: Quantum Dynamics, 2020

Standard homogeneous C*-algebras as compact quantum metric spaces

Author(s): Konrad Aguilar, Tristan Bice
Published in: Quantum Dynamics, 2020

Some applications of conditional expectations to convergence for the quantum Gromov-Hausdorff propinquity

Author(s): Konrad Aguilar, Frederic Latremoliere
Published in: Quantum Dynamics, 2020

Translations in quantum groups

Author(s): Alexandru Chirvasitu
Published in: Quantum Dynamics, 2020

From Hopf algebras to topological quantum groups. A short history, various aspects and some problems

Author(s): Alfons Van Daele
Published in: Quantum Dynamics, 2020

A spectral triple for noncommutative compact surfaces

Author(s): Fredy Díaz García, Elmar Wagner
Published in: Quantum Dynamics, 2020

A note on the injectivity of action by compact quantum groups on a class of C∗-algebras

Author(s): D Goswami, S Joardar
Published in: Quantum Dynamics, 2020

A graded pullback structure of Leavitt path algebras of trimmable graphs

Author(s): Piotr M. Hajac, Atabey Kaygun, Mariusz Tobolski
Published in: Quantum Dynamics, 2020

Pullbacks of graph C*-algebras from admissible pushouts of graphs

Author(s): Piotr M. Hajac, Sarah Reznikoff, Mariusz Tobolski
Published in: Quantum Dynamics, 2020

The asymptotic Connes-Moscovici characteristic map and the index cocycles

Author(s): Atabey Kaygun, Serkan Sütlü
Published in: Quantum Dynamics, 2020

K-theory of cluster C*-algebras

Author(s): Igor Nikolaev
Published in: Quantum Dynamics, 2020

Epsilon factors as algebraic characters on the smooth dual of GLn

Author(s): Roger Plymen
Published in: Quantum Dynamics, 2020

A Note on the Quantum Family of Maps

Author(s): Albert Jeu-Liang Sheu, Thomas Timmermann
Published in: Quantum Dynamics, 2020

Equivariant Dimensions of Graph C*-algebras

Author(s): Alexandru Chirvasitu, Benjamin Passer, Mariusz Tobolski
Published in: The Journal of Functional Analysis, 2020, ISSN 0022-1236

Invariant quantum measure on q-deformed twisted adjoint orbits

Author(s): Kenny De Commer
Published in: Representation Theory, 2020, ISSN 1088-4165

Twisted Dirac operator on quantum SU(2) in disc coordinates

Author(s): Ulrich Kraehmer, Elmar Wagner
Published in: Operator Theory: Advances and Applications, 2020, ISSN 2543-0483

Vector Bundles over Multipullback Quantum Complex Projective Spaces

Author(s): Albert Jeu-Liang Sheu
Published in: Journal of Noncommutative Geometry, 2020, ISSN 1661-6952

Global symbolic calculus of pseudo-differential operators on homogeneous vector bundles

Author(s): Mitsuru Wilson
Published in: SIGMA, 2020, ISSN 1815-0659

The classification of Rokhlin flows on C*-algebras

Author(s): Gabor Szabo
Published in: Communications in Mathematical Physics, 2020, ISSN 1432-0916

Noncommutative Borsuk-Ulam-type conjectures revisited

Author(s): Ludwik Dąbrowski, Piotr M. Hajac, Sergey Neshveyev
Published in: JOURNAL OF NONCOMMUTATIVE GEOMETRY, 2020, ISSN 1661-6960
DOI: 10.4171/jncg/xxx

Deliverables

Publications

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