Lista referatów

• 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...

• 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...

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