North Atlantic Noncommutative Geometry Seminar

April 16, 2025, 5:15 p.m.
ROBERTA ISEPPI (Georg-August-Universität Göttingen, Germany)
FIRST STEPS TOWARDS THE QUANTISATION OF THE SPECTRAL ACTION: THE BATALIN-VILKOVISKY CONSTRUCTION OF FINITE SPECTRAL TRIPLES (FIRST STEPS TOWARDS THE QUANTISATION OF THE SPECTRAL ACTION: THE BATALIN-VILKOVISKY CONSTRUCTION OF FINITE SPECTRAL TRIPLES)
The quantisation of the spectral action associated with spectral triples remains a largely open problem. Even within a perturbative framework, significant complications arise in the presence of non-abelian gauge symmetries. This is precisely where the …

April 9, 2025, 5:15 p.m.
IVÁN RUIZ CAMPOS (Universidad de Málaga, Spain)
ASSOCIATIVE COMMUTATIVE REPRESENTATIONS OF EVOLUTION ALGEBRAS IN DIMENSION TWO (ASSOCIATIVE COMMUTATIVE REPRESENTATIONS OF EVOLUTION ALGEBRAS IN DIMENSION TWO)
In this talk, we study the faithful associative commutative (unitary) representations of evolution algebras of dimension two. This analysis involves the computation of the (tight) p−algebra associated with any 2-dimensional evolution algebra, whenever it exists. …

April 2, 2025, 5:15 p.m.
MARIUSZ TOBOLSKI (Uniwersytet Wrocławski, Poland)
GLUING TOPOLOGICAL-GRAPH C*-ALGEBRAS (GLUING TOPOLOGICAL-GRAPH C*-ALGEBRAS)
Katsura's topological-graph C*-algebras generalize graph C*-algebras and homeomorphism C*-algebras. In this talk, I will present a class of topological-graph C*-algebras coming from noncommutative topology that are not graph C*-algebras, notably the C*-algebras of odd-dimensional Hong-Szymański …

March 26, 2025, 5:15 p.m.
ŁUKASZ KACZMARCZYK (Uniwersytet Warszawski, Poland)
INFORMATION GEOMETRY OF BAYESIAN UPDATING AND REPLICATION (INFORMATION GEOMETRY OF BAYESIAN UPDATING AND REPLICATION)
In this talk, I will show that the Kullback-Leibler divergence can be promoted to a functor from probabilistic spaces to convex polyhedra with a distinguished convex function. Both domain and codomain of this functor enjoy …

March 19, 2025, 5:15 p.m.
GÁBOR ETESI (Budapesti Műszaki és Gazdaságtudományi Egyetem, Hungary)
AN OPERATOR ALGEBRAIC CHARACTERIZATION OF THE VACUUM EINSTEIN EQUATION IN FOUR DIMENSIONS (AN OPERATOR ALGEBRAIC CHARACTERIZATION OF THE VACUUM EINSTEIN EQUATION IN FOUR DIMENSIONS)
In this talk, a new approach to the vacuum Einstein equation on four dimensional Riemannian manifolds (i.e. the Einstein condition on a four dimensional Riemannian metric) is offered in the framework of dynamical systems on …

March 12, 2025, 5:15 p.m.
JACOPO BASSI (MPAN, Warszawa, Poland)
ON ISOMETRIES FOR SPECTRAL TRIPLES ON AF ALGEBRAS (ON ISOMETRIES FOR SPECTRAL TRIPLES ON AF ALGEBRAS)
In this talk, I will discuss some results on the structure of natural non-commutative analogues of groups of isometries for the spectral triples on AF-algebras introduced by Christensen and Ivan. This is a joint work …

March 5, 2025, 5:15 p.m.
MARCELO LACA (University of Victoria, Canada)
A HIGH-TEMPERATURE PHASE TRANSITION FROM NUMBER THEORY (A HIGH-TEMPERATURE PHASE TRANSITION FROM NUMBER THEORY)
Let S be the semidirect product of the multiplicative positive integers acting on the integers, with the operation (a,m)(b,n) = (ab,bm+n), where a and b are positive. In previous joint work with Astrid an Huef …

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 …