Lista referatów

• 2022-03-02, godz. 17:15, ZOOM

  YANG LIU (SISSA)

  CYCLIC STRUCTURE BEHIND THE MODULAR GAUSSIAN CURVATURE

  The modular Gaussian curvature on noncommutative two-tori introduced by Connes and Moscovici leads to a functional relation derived from its variational nature, which is a novel feature purely due to the noncommutativity. I will begin with the differential calculus behind the curvature computation, ...

• 2022-01-26, godz. 17:15, ZOOM

  TOMASZ MASZCZYK (Uniwersytet Warszawski)

  THE MULTIPLICATIVE K-THEORY TYPE OF QUANTUM CW-COMPLEXES

  We enhance current noncommutative methods in topology to distinguish some very different classical homotopy types (e.g., a disconnected and a connected one) of finite CW-complexes, which cannot be distinguished using the Kasparov KK-theory. We achieve this by constructing a noncommutative counterpar...

• 2022-01-19, godz. 17:15, ZOOM

  SOPHIE EMMA MIKKELSEN (Syddansk Universitet)

  ON THE CLASSIFICATION OF QUANTUM LENS SPACES

  There are many noncommutative deformations of classical spaces. For instance, the C*-algebras of quantum lens spaces can be defined as fixed-point subalgebras of the C*-algebras of Vaksman-Soibelman quantum spheres under actions of finite cyclic groups. Hong and Szymański described both the quantum...

• 2022-01-12, godz. 17:15, ZOOM

  BRAM MESLAND (Universiteit Leiden)

  NONCOMMUTATIVE RIEMANNIAN PRINCIPAL BUNDLES

  In this talk, I will present a notion of principal G-spectral triple, with G a compact Lie group, put forward in my joint work with B. Ćaćić (New Brunswick). Our notion connects the algebraic approach to noncommutative principal bundles via principal comodule algebras and strong connections to th...

• 2021-12-22, godz. 17:15, ZOOM

  JONATHAN ROSENBERG (University of Maryland)

  POSITIVE SCALAR CURVATURE ON MANIFOLDS WITH BOUNDARY

  Since work of Gromov and Lawson around 1980, we have known (under favorable circumstances) necessary and sufficient conditions for a closed manifold to admit a Riemannian metric of positive scalar curvature, but not much was known about analogous results for manifolds with boundary (and suitable bou...

• 2021-12-15, godz. 17:15, ZOOM

  ADAM SIKORA (SUNY Buffalo)

  STATED SKEIN ALGEBRAS AND A GEOMETRIC APPROACH TO QUANTUM GROUPS

  We introduce the theory of stated SL(n)-skein algebras of surfaces, which provide a geometric/combinatorial interpretation for the quantum groups Oq(sl(n)) and other related notions from quantum algebra. They also quantize the SL(n)-character varieties of surfaces, are examples o...

• 2021-12-08, godz. 17:15, ZOOM

  PIOTR M. HAJAC (IMPAN)

  THE K-THEORY TYPE OF QUANTUM CW-COMPLEXES

  The CW-complex structure of topological spaces not only reveals how they are built, but also is a natural tool to compute and unravel their K-theory. Therefore, it is desirable to define a noncommutative version of the CW-complex that would play a similar role in noncommutative topology. From some q...

• 2021-12-01, godz. 17:15, ZOOM

  EDUARD VILALTA (Universitat Autònoma de Barcelona)

  COVERING DIMENSION FOR CUNTZ SEMIGROUPS

  In this talk, I will present a notion of covering dimension for Cuntz semigroups and give an overview of the results found thus far. This dimension is always bounded by the nuclear dimension of the associated C*-algebra and, in the case of subhomogeneous C*-algebras, the two dimensions agree. For se...

• 2021-11-24, godz. 17:15, zoom

  ARKADIUSZ BOCHNIAK (Uniwersytet Jagielloński)

  QUANTUM CORRELATIONS ON QUANTUM SPACES

  For given quantum spaces, we study the quantum space of maps between them. We prove that, under certain conditions, the C*-algebra of this quantum space enjoys the lifting property and is residually finite dimensional. We construct a universal operator system inside this C*-algebra, and unravel its ...

• 2021-11-17, godz. 17:15, zoom

  MARIUSZ TOBOLSKI (Uniwersytet Wrocławski)

  NONCOMMUTATIVE PRINCIPAL BUNDLES: BEYOND THE COMPACT CASE

  The notion of a compact noncommutative (or quantum) principal bundle, which generalizes the Cartan compact principal bundle from topology (local triviality not assumed), emerged in the literature almost 30 years ago. Recently, the difficulty of introducing the local-triviality condition to the nonco...

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