North Atlantic Noncommutative Geometry Seminar

April 24, 2024, 5:15 p.m.
LUCAS HALL (University of Haifa, Israel)
TOPOLOGICAL CLASSIFICATION OF SKEW PRODUCTS FOR QUIVER C*-ALGEBRAS
I will present a topological version of the combinatorial skew product for graphs, show how this designs a natural coaction on the C*-algebra associated to a topological quiver, and show natural criteria for identifying an …

April 17, 2024, 5:15 p.m.
TOMASZ BRZEZIŃSKI (Prifysgol Abertawe, Cymru)
HOPF HEAPS AND HOPF ALGEBRAS OF TRANSLATIONS
Grunspan and Schauenburg have proven that quantum torsors (introduced by the former) are closely connected with Hopf-Galois objects. In this talk, I will present, in part, the dualisation of this connection and, in part, a …

April 10, 2024, 5:15 p.m.
CATERINA CONSANI (Johns Hopkins University, Baltimore, USA)
PRIMES, KNOTS AND THE SCALING SITE
The scaling site and its periodic orbits of length log p provide a geometric construction where one can interpret the well-known analogy between primes and knots. The role of the maximal abelian cover of the …

April 3, 2024, 5:15 p.m.
RAIMAR WULKENHAAR (Universität Münster, Germany)
QUANTUM FIELDS ON NONCOMMUTATIVE GEOMETRIES
Quantum field theories (QFT) in four dimensions tend to be trivial or difficult, and often both. QFT on noncommutative geometries provide new examples to explore. They are not admissible examples in the strict sense of …

March 27, 2024, 5:15 p.m.
BORIS L. TSYGAN (Northwestern University, Evanston, USA)
NONLINEAR HOCHSCHILD AND CYCLIC HOMOLOGY
Based on the idea from the eighties due to Loday, Ogle and myself, I introduce a new version of Hochschild and cyclic homology that seems to be closely related to algebraic K-theory. Potential applications include …

March 20, 2024, 5:15 p.m.
EUSEBIO GARDELLA (Chalmers Tekniska Högskola, Göteborg, Sweden)
CLASSIFIABILITY OF CROSSED PRODUCTS
To every action of a discrete group on a compact Hausdorff space one can canonically associate a C*-algebra, called the crossed product. The crossed-product construction is extremely popular, and there are numerous results in the …

March 13, 2024, 5:15 p.m.
PAOLO ASCHIERI (Università del Piemonte Orientale, Alessandria, Italy)
NONCOMMUTATIVE PRINCIPAL BUNDLES OVER PROJECTIVE BASES AND THEIR DIFFERENTIAL CALCULI
We present a sheaf approach to noncommutative principal bundles, and extend it to differential calculi. This allows us to study the differential geometry of noncommutative bundles over noncommutative projective varieties. The main class of examples …

March 6, 2024, 5:15 p.m.
RUDRADIP BISWAS (University of Warwick, England)
SOME HOPF-ALGEBRA INVARIANTS AND NEW RESULTS ON THEIR RELATIONS WITH EACH OTHER
In 1987, two very interesting invariants, called silp (supremum over the injective dimension of projectives) and spli (supremum over the projective dimension of injectives) were introduced for general rings by Gedrich and Gruenberg, and a …

Feb. 28, 2024, 5:15 p.m.
ANDREW MCKEE (Uniwersytet w Białymstoku, Poland)
BANACH ALGEBRAS CONSTRUCTED FROM GROUPOIDS
I will explain recent joint work with K. Bardadyn and B. Kwaśniewski associating Banach algebras to (twisted) groupoids. After showing the construction, I will try to demonstrate that these objects are interesting by answering several questions. Firstly, what is …

Jan. 24, 2024, 5:15 p.m.
GIUSEPPE DE NITTIS (Pontificia Universidad Católica de Chile, Santiago, Chile)
THE MAGNETIC SPECTRAL TRIPLE: APPLICATIONS AND OPEN QUESTIONS
Since the early works by Bellissard, noncommutative geometry has proved to be an excellent tool for the study of the topological phases of matter in general, and for the analysis of the quantum Hall effect …

Jan. 17, 2024, 5:15 p.m.
DEVARSHI MUKHERJEE (Universidad de Buenos Aires, Argentina)
ON p-ADIC OPERATOR ALGEBRAS
Building on the recent definition of a p-adic analogue of a separable Hilbert space by Thom and Claussnitzer, we introduce non-separable p-adic Hilbert spaces and define an algebra of bounded operators on such spaces. This sets up …

Jan. 10, 2024, 5:15 p.m.
JOOST VERCRUYSSE (Université Libre de Bruxelles, Belgium)
GENERALIZATIONS OF YETTER-DRINFEL'D MODULES AND THE CENTER CONSTRUCTION OF MONOIDAL CATEGORIES
A Yetter-Drinfel'd module over a bialgebra H is both a module and a comodule over H satisfying a particular compatibility condition. It is well known that the category of Yetter-Drinfel'd modules (say, over a finite-dimensional Hopf algebra H) is equivalent …

Dec. 20, 2023, 5:15 p.m.
ELMAR WAGNER (Universidad Michoacana, Mexico)
THE SCHOCHET SPECTRAL SEQUENCE FOR NONCOMMUTATIVE CW-COMPLEXES
Noncommutative CW-Complexes can be constructed by dualizing the classical construction and allowing the C*-algebras to be noncommutative. Then the topological invariants, such as K-groups, can be determined up to the ambiguity of group extensions involving …

Dec. 13, 2023, 5:15 p.m.
EHUD MEIR (University of Aberdeen, Scotland)
GEOMETRIC METHODS IN BRAIDED VECTOR SPACES AND THEIR NICHOLS ALGEBRAS
The Nichols algebra of a braided vector space is a generalization of both the symmetric algebra and the exterior algebra. It can be realized as a Hopf algebra in some braided monoidal category. By the …

Dec. 6, 2023, 5:15 p.m.
MATTHIAS SCHÖTZ (IMPAN, Warszawa, Poland)
ASSOCIATIVITY AND COMMUTATIVITY OF PARTIALLY ORDERED RINGS
There are some classical results about automatic associativity and commutativity of ordered rings. In particular, they are established for some lattice-ordered rings in the uniformly bounded case, i.e. for f-rings and for totally ordered skew fields. …