North Atlantic Noncommutative Geometry Seminar

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 …

April 21, 2021, 5:15 p.m.
MAGNUS GOFFENG (Lunds Universitet)
UNTWISTING SPECTRAL TRIPLES
Connes and Moscovici introduced twisted spectral triples over a decade ago as a way of extending spectral noncommutative geometry of finite spectral dimension to situations where no finitely summable spectral triples exist. While there are attractive examples where twisted spectral triples provide a natural noncommutative geometry, one might …

April 14, 2021, 5:15 p.m.
KONRAD AGUILAR (Pomona College)
BUNCE-DEDDENS ALGEBRAS AS QUANTUM-GROMOV-HAUSDORFF-DISTANCE LIMITS OF CIRCLE ALGEBRAS
We show that Bunce-Deddens algebras, which are AT-algebras, are also limits of circle algebras for Rieffel's quantum Gromov-Hausdorff distance, and moreover, form a continuous family indexed by the Baire space. To this end, we endow Bunce-Deddens algebras with a quantum metric structure, a step which requires that we reconcile the …

April 7, 2021, 5:15 p.m.
ANDRZEJ SITARZ (Uniwersytet Jagielloński)
THE RIEMANNIAN GEOMETRY OF A DISCRETIZED CIRCLE AND TORUS
Since the inception of noncommutative geometry, the generalization of Riemannian geometry to the noncommutative setup was a challenge. In this talk, we propose techniques that allow us to provide a complete classification of all linear connections for the minimal …

March 31, 2021, 5:15 p.m.
GUILLERMO CORTIÑAS (Universidad de Buenos Aires)
LEAVITT PATH ALGEBRAS AND THE ALGEBRAIC KIRCHBERG-PHILLIPS PROBLEM
The Kirchberg-Phillips theorem says that unital separable nuclear purely infinite simple C*-algebras in the UCT class are classified by their (topological, C*-algebraic) K-theory and, more generally, that any two separable nuclear purely infinite simple C*-algebras that are KK-isomorphic are …

March 24, 2021, 5:15 p.m.
FRÉDÉRIC LATRÉMOLIÈRE (University of Denver)
FINITE-DIMENSIONAL APPROXIMATIONS OF SPECTRAL TRIPLES ON QUANTUM TORI
The asymptotic behavior of matrix models, as their dimension grows to infinity, is of common interest in mathematical physics. The formalization of the study of limits of finite-dimensional quantum spaces, endowed with some geometric structure, can be done …

March 17, 2021, 5:15 p.m.
SERGEY NESHVEYEV (Universitetet i Oslo)
QUANTIZATION OF COMPACT SYMMETRIC SPACES: TWO APPROACHES
I will explain two ways of quantizing compact symmetric spaces. The first is due to Letzter and Kolb, giving explicit generators of the dual coideal. The second is essentially due to Enriquez and Etingof, and relies on cyclotomic Knizhnik-Zamolodchikov equations. …

March 3, 2021, 5:15 p.m.
ADAM DOR-ON (Københavns Universitet)
OPERATOR ALGEBRAS OF SUBPRODUCT SYSTEMS BY EXAMPLE
In this talk, we will discuss subproduct systems as introduced by Shalit and Solel in 2009 following a definition given by Bhat and Mukherjee. Subproduct systems were originally defined for the purpose of classifying CP-semigroups, but they also give rise to natural …

Jan. 27, 2021, 5:15 p.m.
SØREN EILERS (Københavns Universitet)
A USER'S GUIDE TO THE CLASSIFICATION OF GRAPH C*-ALGEBRAS
Graph C*-algebras (and their precursors, the Cuntz-Krieger algebras) are ubiquitous in modern C*-algebra theory and pop up regularly in noncommutative geometry and/or as models for quantum groups and spaces. In recent years, there has been significant progress concerning the classification of graph C*-algebras by …

Jan. 20, 2021, 5:15 p.m.
MORITZ WEBER (Universität des Saarlandes)
QUANTUM SYMMETRIES OF GRAPHS
We give an introduction to quantum automorphism groups of finite graphs, and then survey recent developments. Amongst others, we mention quantum permutation matrices, tools for detecting quantum symmetries of graphs, links with quantum information theory, quantum isomorphisms of graphs, a quantum Lovász Theorem, and finally quantum symmetries of graph C*-algebras and of quantum-graph C*-algebras. https://www.youtube.com/watch?v=SPXYX-SCAHc