North Atlantic Noncommutative Geometry Seminar

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 …

June 2, 2021, 5:15 p.m.
ALAIN CONNES (IHÉS / Collège de France)
SPECTRAL TRIPLES AND ZETA-CYCLES
This is joint work with C. Consani. When contemplating the low lying zeros of the Riemann zeta function one is tempted to speculate that they may form the spectrum of an operator of the form …

May 26, 2021, 5:15 p.m.
ADAM M. MAGEE (SISSA)
RECENT PROGRESS IN TWISTED REAL STRUCTURES FOR SPECTRAL TRIPLES
Within the approach to NCG based on Connes' spectral triples, real spectral triples, where the addition of a so-called real structure allows the differentiation between spin^c and spin structures and refines the K-homology, are of particular interest. Twisted real structures are a generalisation of these real structures. In this talk, I will give …

May 19, 2021, 5:15 p.m.
ALEXANDER GOROKHOVSKY (University of Colorado Boulder)
THE HEISENBERG CALCULUS AND CYCLIC COHOMOLOGY
On a compact contact manifold, a pseudodifferential operator in the Heisenberg calculus with an invertible symbol is a hypoelliptic Fredholm operator. The index theory of Heisenberg elliptic operators has been extensively investigated from various perspectives. In this talk, I will …

May 12, 2021, 5:15 p.m.
LAURA MANČINSKA (Københavns Universitet)
QUANTUM ENTANGLEMENT, GAMES, AND GRAPH ISOMORPHISMS
Entanglement is one of the key features of quantum mechanics. We will see that nonlocal games provide a mathematical framework for studying entanglement and the advantage that it can offer. We will then take a closer look at graph-isomorphism games where two provers aim to …

May 5, 2021, 5:15 p.m.
GUOLIANG YU (Texas A&M University)
QUANTITATIVE K-THEORY, K-HOMOLOGY AND THEIR APPLICATIONS
I will give an introduction to quantitative K-theory, K-homology and their applications. In particular, I will discuss my recent joint work with Rufus Willett on the universal coefficient theorem for nuclear C*-algebras. If time allows, I will also talk about other …

April 28, 2021, 5:15 p.m.
JACK SPIELBERG (Arizona State University)
AF ALGEBRAS ASSOCIATED TO ORIENTED COMBINATORIAL DATA
One of the remarkable features of the construction of C*-algebras from directed graphs is the characterization of approximate finite dimensionality: the C*-algebra is AF if and only if the graph has no directed cycle. This construction has been …