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NCG&T Prague

usually takes place each Tuesday at 16:00 Institute of Mathematics CAS, Blue lecture room,  Zitna  25, Praha 1
Chair: Tristan Bice, Karen Stung

What is noncommutative geometry and topology? The idea stems from the Gelfand theorem which states that the category of compact Hausdorff spaces and commutative C*-algebras are dual. If we drop the condition of commutativity from our C*-algebras, we arrive at the notion of a noncommutative topological space. This can be carried further into the realm of noncommutative of geometry by equipping *-algebras with geometric structures.
Our research focusses on both quantum algebraic and operator algebraic aspects of noncommutative geometry and topology. This includes research in Hopf algebras, quantum groups, and noncommutative complex geometry, while on the operator algebra side, we study C*-algebras, with particular focus on C*-algebras arising from dynamical constructions such as minimal actions, groupoids, and semigroups.
Partially supported by GAČR project 20-17488Y Applications of C*-algebra classification: dynamics, geometry, and their quantum analogues and PRIMUS grant Spectral Noncommutative Geometry of Quantum Flag Manifolds.

Constructions from C*-correspondences over commutative C*-algebras

Marzieh Forough
Czech Technical University in Prague
Tuesday, 1. February 2022 - 16:00 to 17:00
This talk will take place in the blue seminar room, back building, Žitna 25.

It will also be broadcast on Zoom:
Meeting ID: 919 7518 3920
Passcode: 102707
In this talk I will show how one constructs C*-algebras from C*-correspondences over a commutative C*-algebra C(X). A particularly tractable type of correspondence comes from the module of sections of a vector bundle where multiplication on one side of the module is given by composition by a homeomorphism α:X→X. When X is an infinite compact metric space with finite covering dimension and α is minimal, the resulting C*-algebras are classifiable by Elliott invariants. I will discuss this and related results, which is based on joint work with Adamo, Archey, Georgescu, Jeong, Strung and Viola and certain subsets thereof.

Levi-Civita connections on tame differential calculi

Sugato Mukhopadhyay
Institute of Mathematics of the Polish Academy of Sciences
Tuesday, 8. February 2022 - 16:00
This talk will take place in the blue seminar room, back building, Žitna 25 and on Zoom.
Meeting ID: 919 7518 3920
Passcode: 102707
The notion of tame spectral triples and that of Levi-Civita connections defined on them will be presented. We will discuss a result on the existence and uniqueness of these Levi-Civita connections, along with examples at our disposal. We will conclude with a report of further developments on a class of differential calculi that have since come to be known as tame differential calculi.

This talk is based on a joint work with Jyotishman Bhowmick and Debashish Goswami, and a subsequent one with Suvrajit Bhattacharjee and Soumalya Joardar.

Quantum orbit method in non standard complex projective spaces

Nicola Ciccoli
University of Perugia
Tuesday, 15. February 2022 - 16:00 to 17:00
This talk will take place on Zoom.
Meeting ID: 919 7518 3920
Passcode: 102707
Non standard quantum complex projective spaces are a 1-parameter family of coisotropic quotients of standard SU_q(n) . We will discuss how to construct a homemorphism between the leaf space of the underlying Poisson structure and the unitary dual of the quantized C^*-algebra of functions. Results will be obtained in the framework of groupoid quantization.

Classical spaces and quantum symmetry

Amaury Freslon
Université Paris-Sud
Tuesday, 22. February 2022 - 16:00
This talk will take place in the blue seminar room, back building, Žitna 25 and on Zoom.
Meeting ID: 919 7518 3920
Passcode: 102707
One direction of research in the theory of quantum groups is to use them as generalized symmetries of spaces. For non-commutative spaces, this has lead to the discovery of very important examples but for classical spaces the picture is less clear. While finite spaces are known to have quantum symmetries embodied in Wang’s quantum permutation group, many classical spaces have been proven to have no quantum symmetry. In this talk I will survey some results on that topic and present recent progress obtained in collaboration with F. Taipe and S. Wang. We prove that the quantum permutation group cannot act ergodically on a connected classical compact space, answering a question of Goswami as modified by Huang. The proof uses tools which are very different from the usual ones in quantum rigidity theory and rely on a categorical description of ergodic actions of compact quantum groups.