North Atlantic Noncommutative Geometry Seminar

June 1, 2022, 5:15 p.m.
ELMAR SCHROHE (Leibniz Universität Hannover))
ORDER PRESERVING AUTOMORPHISMS OF SHUBIN TYPE PSEUDODIFFERENTIAL OPERATORS
We consider the algebra of all classical Shubin type pseudodifferential operators on Euclidean space. Following up on a remarkable result of Duistermaat and Singer (Comm. Pure Appl. Math. XXVIV:39-47, 1976) for the case of the …

May 25, 2022, 5:15 p.m.
EVGENIOS T. A. KAKARIADIS (Newcastle University)
MORITA EQUIVALENCE FOR OPERATOR SYSTEMS
In ring theory, Morita equivalence preserves many properties of the objects, and generalizes the isomorphism equivalence between commutative rings. A strong Morita equivalence for selfadjoint operator algebras was introduced by Rieffel in the 60s, and …

May 18, 2022, 5:15 p.m.
JENS KAAD (Syddansk Universitet)
GROUP COCYCLES ON LOOP GROUPS
In this talk, we start out by reviewing the construction of central extensions of smooth loop groups and their relationship to the tame symbol of a pair of meromorphic functions on a Riemann surface. Our …

May 11, 2022, 5:15 p.m.
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 …

May 4, 2022, 5:15 p.m.
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 …

April 27, 2022, 5:15 p.m.
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 …

April 20, 2022, 5:15 p.m.
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 …

April 13, 2022, 5:15 p.m.
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 …

April 6, 2022, 5:15 p.m.
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 …

March 30, 2022, 5:15 p.m.
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 …

March 23, 2022, 5:15 p.m.
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 …

March 16, 2022, 5:15 p.m.
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 …

March 9, 2022, 5:15 p.m.
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 …

March 2, 2022, 5:15 p.m.
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 …

Jan. 26, 2022, 5:15 p.m.
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 …