North Atlantic Noncommutative Geometry Seminar

Nov. 12, 2025, 5:15 p.m.
JENS KAAD (Syddansk Universitet, Odense, Denmark)
SPECTRAL LOCALIZERS IN KK-THEORY (SPECTRAL LOCALIZERS IN KK-THEORY)
In this talk, we compute the index homomorphism of even K-groups arising from a class in even KK-theory via the Kasparov product. Due to the seminal work of Baaj and Julg, under mild conditions on …

Nov. 5, 2025, 5:15 p.m.
MARIUSZ TOBOLSKI (Uniwersytet Wrocławski, Wrocław, Poland)
LOCALLY DERIVED GRAPHS (LOCALLY DERIVED GRAPHS)
Voltage and derived graphs (also called base and skew product graphs, respectively) were introduced by Gross and Tucker to study free actions of groups on graphs. These notions found applications in the theory of C*-algebras …

Oct. 29, 2025, 5:15 p.m.
ZACHARY MESYAN (University of Colorado, Colorado Springs, USA)
POSETS FROM LEAVITT PATH ALGEBRAS AND GRAPH INVERSE SEMIGROUPS (POSETS FROM LEAVITT PATH ALGEBRAS AND GRAPH INVERSE SEMIGROUPS)
We discuss parallel developments in the study of three types of well-known algebraic objects built from directed graphs: Leavitt path algebras, graph inverse semigroups, and graph C*-algebras. Similar results have been proved about those objects, …

Oct. 22, 2025, 5:15 p.m.
FRANCESCO D'ANDREA (Università di Napoli Federico II, Italy)
ON AMPLIFIED-GRAPH C*-ALGEBRAS AS CORES OF CUNTZ-KRIEGER ALGEBRAS (ON AMPLIFIED-GRAPH C*-ALGEBRAS AS CORES OF CUNTZ-KRIEGER ALGEBRAS)
Given a finite directed acyclic graph R, we construct from it two graphs: the graph E obtained by adding a loop at every vertex of R and the graph F obtained by replacing every edge …

Oct. 15, 2025, 5:15 p.m.
ELMAR WAGNER (Universidad Michoacana de San Nicolás de Hidalgo, Morelia, Mexico)
THE BGG RESOLUTION AND THE SPECTRUM OF DIRAC-LAPLACIANS ON NONCOMMUTATIVE LINE BUNDLES (THE BGG RESOLUTION AND THE SPECTRUM OF DIRAC-LAPLACIANS ON NONCOMMUTATIVE LINE BUNDLES)
The Bernstein-Gelfand-Gelfand resolution is a powerful tool to define natural elliptic first-order differential operators (Dirac operators) on irreducible flag manifolds. Heckenberger and Kolb showed in 2006 that the same construction applies to noncommutative irreducible flag …

Oct. 8, 2025, 5:15 p.m.
MICHAŁ ZIEMBOWSKI (Politechnika Warszawska, Warszawa, Poland)
FROM MATRICES TO LEAVITT PATH ALGEBRAS: BUILDING MAXIMAL COMMUTATIVE SUBALGEBRAS (FROM MATRICES TO LEAVITT PATH ALGEBRAS: BUILDING MAXIMAL COMMUTATIVE SUBALGEBRAS)
We move from the classical matrix setting to new constructions in Leavitt path algebras to investigate maximal commutative subalgebras. As a starting point, we recall the Schur-Jacobson viewpoint on maximal commutative subalgebras of matrix algebras, …

June 11, 2025, 5:15 p.m.
GILLES GONÇALVES DE CASTRO (Universidade Federal de Santa Catarina, Florianópolis, Brazil)
RELATION MORPHISMS OF DIRECTED GRAPHS (RELATION MORPHISMS OF DIRECTED GRAPHS)
Associating graph algebras to directed graphs leads to both covariant and contravariant functors from suitable categories of graphs to the category k-Alg of algebras and algebra homomorphisms. As both functors are often used at the …

June 4, 2025, 5:15 p.m.
ELIEZER BATISTA (Universidade Federal de Santa Catarina, Florianópolis, Brazil)
LOCAL BISECTIONS OF HOPF ALGEBROIDS AND INVERSE SEMIGROUPS (LOCAL BISECTIONS OF HOPF ALGEBROIDS AND INVERSE SEMIGROUPS)
The relationship between étale groupoids and inverse semigroups via local bisections has been known for a long time. In particular, there is an adjunction between the category of étale groupoids with morphisms defined from actions …

May 28, 2025, 5:15 p.m.
FABIO EUGENIO GIOVANNI CIPRIANI (Politecnico di Milano, Italy)
THE ENERGY OF VECTOR BUNDLES (THE ENERGY OF VECTOR BUNDLES)
Using ideas of (noncommutative) potential theory, we introduce the concept of energy E(V) of a vector bundle V over a Riemannian manifold and, more generally, over a Dirichlet space. We show that, in low dimension, …

May 21, 2025, 5:15 p.m.
MARKUS B. FRÖB (Universität Leipzig, Germany)
NON-COMMUTATIVE COORDINATES FROM PERTURBATIVE QUANTUM GRAVITY (NON-COMMUTATIVE COORDINATES FROM PERTURBATIVE QUANTUM GRAVITY)
Local observables in (perturbative) quantum gravity are notoriously hard to define, since the gauge symmetry of gravity (diffeomorphisms) moves points on the manifold. In particular, this is a problem for backgrounds of high symmetry such …

May 14, 2025, 5:15 p.m.
PAWEL SARKOWICZ (University of Waterloo, Canada)
UNIVERSAL COVERING GROUPS OF UNITARY GROUPS (UNIVERSAL COVERING GROUPS OF UNITARY GROUPS)
We examine a notion from algebraic topology, that of "universal covering groups", with the goal of better understanding unitary groups of C*-algebras. We give a complete description of what these universal covering groups are for …

May 7, 2025, 5:15 p.m.
RUY EXEL (Universidade Federal de Santa Catarina, Florianópolis, Brazil)
FLOWS ON UNIFORM ROE ALGEBRAS (FLOWS ON UNIFORM ROE ALGEBRAS)
For a uniformly locally finite metric space (X,d), we investigate coarse flows on its uniform Roe algebra C*ᵤ(X), defined as one-parameter groups of automorphisms whose differentiable elements include all partial isometries arising from partial translations …

April 30, 2025, 5:15 p.m.
EUN JI KANG (Seoul National University, South Korea)
A CATEGORICAL INTERPRETATION OF CONTINUOUS ORBIT EQUIVALENCE FOR PARTIAL DYNAMICAL SYSTEMS (A CATEGORICAL INTERPRETATION OF CONTINUOUS ORBIT EQUIVALENCE FOR PARTIAL DYNAMICAL SYSTEMS)
We define the orbit morphism of partial dynamical systems, and prove that an orbit morphism being an isomorphism in the category of partial dynamical systems and orbit morphisms is equivalent to the existence of a …

April 23, 2025, 5:15 p.m.
ALCIDES BUSS (Universidade Federal de Santa Catarina, Florianópolis, Brazil)
AMENABILITY OF NON-HAUSDORFF ÉTALE GROUPOIDS AND NUCLEARITY OF THEIR C*-ALGEBRAS (AMENABILITY OF NON-HAUSDORFF ÉTALE GROUPOIDS AND NUCLEARITY OF THEIR C*-ALGEBRAS)
The link between amenability and nuclearity lies at the heart of many structural results in operator algebras. For discrete groups, these notions are famously equivalent via the reduced group C*-algebra. In this talk, I will …

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 …