North Atlantic Noncommutative Geometry Seminar

Jan. 19, 2022, 5:15 p.m.
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. …

Jan. 12, 2022, 5:15 p.m.
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 …

Dec. 22, 2021, 5:15 p.m.
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 …

Dec. 15, 2021, 5:15 p.m.
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 of quantum …

Dec. 8, 2021, 5:15 p.m.
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 …

Dec. 1, 2021, 5:15 p.m.
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 …

Nov. 24, 2021, 5:15 p.m.
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 …

Nov. 17, 2021, 5:15 p.m.
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 …

Nov. 10, 2021, 5:15 p.m.
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 …

Nov. 3, 2021, 5:15 p.m.
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 …

Oct. 27, 2021, 5:15 p.m.
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 …

Oct. 20, 2021, 5:15 p.m.
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 …

Oct. 13, 2021, 5:15 p.m.
TOMASZ MASZCZYK (University of Warsaw)
INERTIAL HOPF-CYCLIC HOMOLOGY
We construct, study and apply a characteristic map from the relative periodic cyclic homology of the quotient map for agroup action to the periodic Hopf-cyclic homology with coefficients associated with the inertia of the action. …

Oct. 6, 2021, 5:15 p.m.
MASOUD KHALKHALI (Western University)
BOOTSTRAPPING DIRAC ENSEMBLES
It is always interesting to find connections between NCG and other central areas of mathematics. Recent work gradually unravels deep connections between NCG and random matrix theory. In this talk, I shall explain certain techniques …

June 9, 2021, 5:15 p.m.
NIGEL HIGSON (Pennsylvania State University)
THE OKA PRINCIPLE AND A K-THEORETIC PERSPECTIVE ON THE LANGLANDS CLASSIFICATION
The Oka principle in complex geometry asserts that continuous structures in a variety of contexts, including vector bundles on polynomially convex sets, carry unique holomorphic structures, up to isomorphism.  The Oka principle fits naturally into …