Geometria niekomutatywna

Ulam Noncommutative Geometry Seminar

Organizator: Piotr M. Hajac

Miejsce: Math 350, CU Boulder, USA

Czas: Poniedziałki, 15:00 - 15:50

 

28 stycznia i 11 lutego 2019, 15:00-15:50

PULLBACKS OF GRAPH C*-ALGEBRAS FROM ADMISSIBLE PUSHOUTS OF GRAPHS

We define an admissible decomposition of a graph E into subgraphs E1 and E2, and consider the intersection graph F as a subgraph of both E1 and E2. We prove that, if the graph E is row finite and its decomposition into the subgraphs E1 and  E2 is admissible, then the graph C*-algebra C*(E) of E is the pullback C*-algebra of the canonical surjections from C*(E1) and C*(E2) onto C*(F). Based on joint work with Sarah Reznikoff and Mariusz Tobolski.

PIOTR M. HAJAC (CU Boulder / IMPAN)

4 lutego 2019, 15:00-15:50

PSEUDO-DIFFERENTIAL OPERATORS AND THEIR SYMBOLS ON Θ-DEFORMATION OF COMPACT LIE GROUPS

In the seminal work of M. Ruzhansky et al., a very suitable pseudo-differential calculus on compact Lie groups was constructed using the Peter-Weyl decomposition of L2 functions. I will explain this formalism, then present my generalization of it to compact quantum groups, which come from the Θ-deformation of compact Lie groups.

MITSURU WILSON (IMPAN)

18 lutego 2019, 15:00-15:50

CONVERGENCE OF SPECTRAL TRIPLES

We present our recent ideas on how to show that a family of metric spectral triples is continuous in the sense of the Gromov-Hausdorff propinquity.

FRÉDÉRIC LATRÉMOLIÈRE (University of Denver)

25 lutego 2019, 15:00-15:50

QUANTUM-RIGID MANIFOLDS

Compact quantum groups are non-commutative spaces with a sufficient amount of structure to resemble classical compact groups and recover much of their behavior. Their actions on classical or non-commutative spaces capture "quantum symmetries". I will discuss a curious phenomenon whereby "sufficiently regular" classical structures do not admit genuinely quantum symmetries: a compact quantum group acting in a structure-preserving fashion is automatically an ordinary compact group. This is the case, for instance, for compact quantum groups acting isometrically on the underlying geodesic metric space of a compact connected Riemannian manifold, with or without boundary. (Joint work with Debashish Goswami.)

ALEXANDRU CHIRVASITU (SUNY Buffalo)

4 marca 2019, 15:00-15:50

INDUCTIVE LIMITS OF C*ALGEBRAS AND COMPACT QUANTUM METRIC SPACES

In this talk, we will place quantum metrics, in the sense of Rieffel, on certain unital inductive limits of C*-algebras built from quantum metrics on the terms of the given inductive sequence with certain compatibility conditions. One of these conditions is that the inductive sequence forms a Cauchy sequence of quantum metric spaces in the dual Gromov-Hausdorff propinquity of Latremoliere. Since the dual propinquity is complete, this will produce a limit quantum metric space. Based on our assumptions, we then show that the C*-algebra of this limit quantum metric space is isomorphic to the given inductive limit, which finally places a quantum metric on the inductive limit. This then immediately allows us to establish a metric convergence of the inductive sequence to the inductive limit. Another consequence to our construction is that we place new quantum metrics on all unital AF algebras that extend our previous work with Latrémolière on unital AF algebras with faithful tracial state.

KONRAD AGUILAR (Arizona State University, Tempe)

11 marca 2019, 15:00-15:50

THE QUANTUM FAMILY OF MAPS

The notion of the quantum space of all maps between quantum spaces was invented by Piotr M. Sołtan. His pioneering work was mainly focused on finite-dimensional C*-algebras, which are matrix-algebra bundles over a finite set S. We propose a generalization of this concept that includes arbitrary compact Hausdorff spaces X (instead of finite sets S) and takes into account the topology of X. In this context, the notion of the free product of copies of a unital C*-algebra topologically indexed by a compact Hausdorff space arises naturally, and enjoys some desired functoriality. Based on joint work with Thomas Timmermann.

ALBERT SHEU (University of Kansas)

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