North Atlantic Noncommutative Geometry Seminar

Feb. 26, 2025, 5:15 p.m.
ARNAUD BROTHIER (Università di Trieste, Italy & UNSW Sydney, Australia)
MODULI OF REPRESENTATIONS OF THE CUNTZ ALGEBRA OBTAINED VIA VAUGHAN JONES TECHNOLOGY (REPRESENTATIONS OF THE CUNTZ ALGEBRA OBTAINED VIA VAUGHAN JONES TECHNOLOGY)
In his quest to construct quantum field theories from subfactors, Vaughan Jones found an unexpected connection with Richard Thompson's group. This led to Jones' technology: a powerful method for constructing actions of certain groups. I …

Jan. 22, 2025, 5:15 p.m.
CARLA FARSI (University of Colorado, Boulder, USA)
METRIC LIMITS OF SPECTRAL TRIPLES AND NONCOMMUTATIVE PRINCIPAL G-BUNDLES (METRIC LIMITS OF SPECTRAL TRIPLES AND NONCOMMUTATIVE PRINCIPAL G-BUNDLES)
The spectral propinquity, a generalization of the Gromov-Hausdorff distance to the realm of noncommutative geometry, is a distance on metric spectral triples developed within the framework of metric noncommutative geometry by Latrémolière. Metric spectral triples …

Jan. 15, 2025, 5:15 p.m.
RYSZARD NEST (Københavns Universitet, Denmark)
AUTOMORPHISMS OF THE BOUTET DE MONVEL ALGEBRA (AUTOMORPHISMS OF THE BOUTET DE MONVEL ALGEBRA)
In a remarkable work in 1976, Duistermaat and Singer studied the algebras of all classical pseudodifferential operators on smooth boundaryless manifolds. They gave a description of order-preserving algebra isomorphism between the algebras of classical pseudodifferential …

Jan. 8, 2025, 5:15 p.m.
TOMASZ MASZCZYK (Uniwersytet Warszawski, Poland)
THE CLIFFORD-DIRAC QUANTIZATION OF THE DE RHAM COMPLEX (THE CLIFFORD-DIRAC QUANTIZATION OF THE DE RHAM COMPLEX)
We show that the de Rham complex is a degeneration of a one parameter family of filtered Z/2Z-graded algebras with a degree one almost derivation that are generically isomorphic to the Clifford algebra equipped with …

Dec. 18, 2024, 5:15 p.m.
PALLE JORGENSEN (University of Iowa, Iowa City, USA)
q-CANONICAL COMMUTATION RELATIONS AND THE STABILITY OF THE CUNTZ ALGEBRA (q-CANONICAL COMMUTATION RELATIONS AND THE STABILITY OF THE CUNTZ ALGEBRA)
Motivated by questions from quantum physics, we study commutation relations with a deformation parameter q. The case q=0 yields the Cuntz relations and the Cuntz algebra. We show that there are C*-isomorphisms for values of …

Dec. 11, 2024, 5:15 p.m.
BENJAMIN ANDERSON-SACKANEY (University of Saskatchewan, Saskatoon, Canada)
C*-SIMPLICITY AND BOUNDARY ACTIONS OF DISCRETE QUANTUM GROUPS (C*-SIMPLICITY AND BOUNDARY ACTIONS OF DISCRETE QUANTUM GROUPS)
A group is C*-simple if its reduced C*-algebra is simple. Two of the most historically important notions used for proving a group is C*-simple are Powers’ averaging property and topologically free boundary actions. These techniques …

Dec. 4, 2024, 5:15 p.m.
MATTHEW KENNEDY (University of Waterloo, Canada)
INTERMEDIATE SUBALGEBRAS FOR REDUCED CROSSED PRODUCTS OF DISCRETE GROUPS (INTERMEDIATE SUBALGEBRAS FOR REDUCED CROSSED PRODUCTS OF DISCRETE GROUPS)
We obtain sufficient and (almost always) necessary conditions for a complete characterization of intermediate subalgebras of reduced crossed products of discrete groups. I will discuss this result as well as some of the key underlying …

Nov. 27, 2024, 5:15 p.m.
DIMITRIS M. GERONTOGIANNIS (IMPAN, Warszawa, Poland)
THE log-LAPLACIAN ON AHLFORS REGULAR SPACES AND NONCOMMUTATIVE BOUNDARIES (THE log-LAPLACIAN ON AHLFORS REGULAR SPACES AND NONCOMMUTATIVE BOUNDARIES)
The Laplace-Beltrami operator is a fundamental tool in the study of compact Riemannian manifolds. In this talk, based on joint work with Bram Mesland (Leiden), I will introduce the logarithmic analogue of this operator on …

Nov. 20, 2024, 5:15 p.m.
ALAIN CONNES (Collège de France and IHES)
FROM CLASS FIELD THEORY TO ZETA SPECTRAL TRIPLES (FROM CLASS FIELD THEORY TO ZETA SPECTRAL TRIPLES)
I will cover recent joint work with C. Consani and H. Moscovici on the long search for spectral triples associated to the low lying zeros of zeta (infrared) as well as to ultraviolet zeros and …

Nov. 13, 2024, 5:15 p.m.
JONAS SCHNITZER (Università di Pavia, Italy)
THE QUANTIZATION OF MOMENTUM MAPS AND ADAPTED FORMALITY MORPHISMS (THE QUANTIZATION OF MOMENTUM MAPS AND ADAPTED FORMALITY MORPHISMS)
If a Lie group acts on a Poisson manifold by Hamiltonian symmetries, there is a well-understood way to get rid of unnecessary degrees of freedom and pass to a Poisson manifold of a lower dimension. …

Nov. 6, 2024, 5:15 p.m.
RALF MEYER (Georg-August Universität Göttingen, Germany)
CORRESPONDENCES BETWEEN GRAPH C*-ALGEBRAS (CORRESPONDENCES BETWEEN GRAPH C*-ALGEBRAS)
We describe proper correspondences from graph C*-algebras to arbitrary C*-algebras by K-theoretic data. If the target C*-algebra is a graph C*-algebra as well, we may lift an isomorphism and its inverse on a certain invariant …

Oct. 30, 2024, 5:15 p.m.
JOHN QUIGG (Arizona State University, Tempe, USA)
THE LADDER (THE LADDER)
We present a new method of establishing a bijective correspondence - in fact, a lattice isomorphism - between invariant ideals of C*-algebras and their crossed products by a fixed locally compact group. It was already …

Oct. 23, 2024, 5:15 p.m.
SUGATO MUKHOPADHYAY (SISSA, Trieste, Italy)
ALGEBRAIC AND SPECTRAL TORSIONS ON THE ALMOST COMMUTATIVE GEOMETRY OF DOUBLED MANIFOLDS
I will present a construction of a noncommutative second order differential calculus on the algebra of smooth functions on the product of a manifold with the two-point space. This involves a modification of the standard …

Oct. 16, 2024, 5:15 p.m.
FRANCESCO D'ANDREA (Università di Napoli Federico II, Italy)
VAKSMAN-SOIBELMAN ODD QUANTUM SPHERES AND COMPLEX QUANTUM PROJECTIVE SPACES REVISITED
Odd-dimensional quantum spheres were introduced in 1990 by Vaksman and Soibelman as quantum homogeneous spaces of Woronowicz's quantum unitary groups. Since then, they have served as major examples for testing ideas about non-commutative spaces. In …

Oct. 9, 2024, 5:15 p.m.
RITA FIORESI (Università di Bologna, Italy)
REDUCTIONS OF QUANTUM PRINCIPAL BUNDLES
We develop the theory of reductions of quantum principal bundles over projective bases. We show how the sheaf-theoretic approach can be effectively applied to certain relevant examples such as the Klein model for the projective …