Lista referatów

• 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...

• 2021-11-10, godz. 17:15, zoom

  FRANCESCA ARICI (Universiteit Leiden)

  SPLIT EXTENSIONS AND KK-EQUIVALENCES FOR QUANTUM PROJECTIVE SPACES

  In this talk, I will describe a construction of an explicit KK-equivalence between the noncommutative C*-algebras of continuous functions on the Vaksman-Soibelman quantum complex projective spaces and their commutative counterparts. The construction relies on general results about KK-equivalences, a...

• 2021-11-03, godz. 17:15, zoom

  ANDREAS KRAFT (IMPAN)

  FIRST STEPS TOWARDS [FORMALITY, REDUCTION]=0?

  One open question in deformation quantization is its compatibility with reduction in the case of Poisson manifolds. In this talk, we propose a way to study this compatibility by investigating the commutativity of a diagram of certain L-infinity-morphisms. On the classical side, one considers the cur...

• 2021-10-27, godz. 17:15, zoom

  SUGATO MUKHOPADHYAY (IMPAN)

  LEVI-CIVITA CONNECTIONS ON TAME DIFFERENTIAL CALCULI

  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...

• 2021-10-20, godz. 17:15, zoom

  ANDRZEJ SITARZ (Uniwersytet Jagielloński)

  SPECTRAL TRIPLES WITH NON-PRODUCT DIRAC OPERATORS

  Models of noncommutative geometry that are beyond the usual almost-commutative framework that assumes product metrics may lead to interesting physical theories in  both particle physics and gravity. In the former, they allow a description of the Standard Model without the fermion doubling, wi...

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