Lista referatów

• 2022-04-13, godz. 17:15, zoom

  JOACHIM CUNTZ (Universität Münster)

  THE IMAGE OF BOTT PERIODICITY IN CYCLIC HOMOLOGY

  We analyze the relationship between Bott periodicity in K-theory and the natural periodicity of cyclic homology. This is a basis for understanding the multiplicativity, in odd dimensions, of a bivariant Chern-Connes character from K-theory to cyclic theory. ...

• 2022-04-06, godz. 17:15, zoom

  WALTER VAN SUIJLEKOM (Radboud Universiteit)

  NONCOMMUTATIVE SPACES AT FINITE RESOLUTION

  We extend the traditional framework of noncommutative geometry in order to deal with two types of approximation of metric spaces. On the one hand, we consider spectral truncations of geometric spaces, while on the other hand, we consider metric spaces up to finite resolution. In our approach, the tr...

• 2022-03-30, godz. 17:15, ZOOM

  ALESSANDRO CAROTENUTO (Univerzita Karlova)

  A BOREL-WEIL THEOREM FOR IRREDUCIBLE QUANTUM FLAG MANIFOLDS

  The Borel-Weil theorem is a fundamental result in (classical) geometric representation theory. It realizes each irreducible representation of a complex semisimple Lie algebra as the space of holomorphic sections over a flag manifold. I will give a noncommutative generalization of the Borel-Weil theo...

• 2022-03-23, godz. 17:15, ZOOM

  RALF MEYER (Universität Göttingen)

  C*-ALGEBRAS DEFINED BY GROUPOID CORRESPONDENCES

  In this talk, I define correspondences between étale groupoids, and show that they contain topological graphs and self-similarities of groups and graphs as special cases. A correspondence between two groupoids induces a C*-correspondence between the groupoid C...

• 2022-03-16, godz. 17:15, ZOOM

  XIANG TANG (Washington University in St. Louis)

  THE HELTON-HOWE TRACE, THE CONNES-CHERN CHARACTER, AND QUANTIZATION

  In the early 70s, Helton and Howe proved a beautiful formula for the trace of commutators of Toeplitz operators. In the 80s, Connes greatly generalized the Helton-Howe trace formula using cyclic cohomology. The Connes-Chern character contains the Helton-Howe trace as the top degree compone...

• 2022-03-09, godz. 17:15, ZOOM

  RYSZARD NEST (Københavns Universitet)

  PROJECTIVE REPRESENTATION THEORY FOR COMPACT QUANTUM GROUPS AND THE BAUM-CONNES ASSEMBLY MAP

  We study the theory of projective representations for a compact quantum group G, i.e. actions of G on B(H) for some Hilbert space H. We show that any such projective representation is inner, and hence is induced by an Ω-twisted representation for some unitary...

• 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...

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