Lista referatów

• 2022-05-11, godz. 17:15, ZOOM

  DAVID KYED (Syddansk Universitet)

  THE NON-COMMUTATIVE METRIC GEOMETRY OF QUANTUM SU(2)

  Rieffel's theory of compact quantum metric spaces provides an elegant non-commutative extension of the classical theory of compact metric spaces that is well aligned with Connes' non-commutative geometry. Recently, the quantum metric structure of q-deformed spaces has begun to unravel. In my...

• 2022-05-04, godz. 17:15, ZOOM

  MAXIM KONTSEVICH (IHÉS)

  ON PERIODS OF NONCOMMUTATIVE ALGEBRAS

  Connes' theory of integration says that a finitely summable Fredholm module defines a linear functional on periodic cyclic homology of an algebra defined over a subfield of complex numbers. Let us assume that the algebra is defined over rational numbers. Then one can show that, in this way, one ...

• 2022-04-27, godz. 17:15, ZOOM

  WOJCIECH SZYMAŃSKI (Syddansk Universitet)

  ON THE CONJUGACY OF MASAS IN GRAPH C*-ALGEBRAS

  We discuss the problem of conjugacy of MASAs in (purely infinite) graph C*-algebras. The main question we are interested in is inner versus outer conjugacy. To attack this problem, we employ a certain technique motivated by von Neumann algebra considerations. We illustrate it with some technically n...

• 2022-04-20, godz. 17:15, zoom

  PAULO CARRILLO ROUSE (Université Paul Sabatier, Toulouse III)

  AN NCG APPROACH TO INDEX THEORY FOR MANIFOLDS WITH CORNERS

  In this talk, I will review my joint work (published and on going) with Jean-Marie Lescure and Mario Velasquez, where we use groupoid and NCG techniques to study some problems in geometric analysis on manifolds with corners. In particular, I will review some K-theory computations (of the algebras of...

• 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...

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