North Atlantic Noncommutative Geometry Seminar

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. …

Nov. 29, 2023, 5:15 p.m.
THOMAS WEBER (Università di Bologna, Italy)
INFINITESIMAL BRAIDINGS AND PRE-CARTIER BIALGEBRAS
We propose an approach to infinitesimal braidings which applies to arbitrary braided monoidal categories. The motivating idea is to understand an infinitesimal braiding as a first order deformation of a given braiding. We call braided …

Nov. 22, 2023, 5:15 p.m.
HERVÉ OYONO-OYONO (Université de Lorraine, Metz, France)
GEOMETRIC DECOMPOSABILITY FOR GROUPOIDS (TBA)
Geometric decomposability for étale groupoids was introduced by E. Guentner, R. Willet and G. Yu. The idea was to generalize the "cut and pasting" strategy developed by G. Yu in his proof of the Novikov …

Nov. 15, 2023, 5:15 p.m.
PETER HOCHS (Radboud Universiteit, Nijmegen, Netherlands)
EQUIVARIANT ANALYTIC TORSION AND AN EQUIVARIANT RUELLE DYNAMICAL ZETA FUNCTION
Analytic torsion was introduced by Ray and Singer as a way to realise Reidemeister-Franz torsion analytically. (The equality was independently proved by Cheeger and Müller.) The Ruelle dynamical zeta function is a topological way to …

Nov. 8, 2023, 5:15 p.m.
MICHAEL FRANCIS (Western University, London, Canada)
THE TRANSVERSE ORIENTATION CLASS OF CERTAIN SINGULAR FOLIATIONS
In the 1980s, Connes defined the transverse orientation class of a transversely oriented foliation and showed it is a non-torsion element in K-theory. We will examine a special family of singular foliations for which a …

Oct. 25, 2023, 5:15 p.m.
STEFAAN CAENEPEEL (Vrije Universiteit Brussel, Belgium)
FORMAL THEORY OF MONADS, ADJUNCTIONS, ENTWINING STRUCTURES AND GALOIS THEORY
Brzeziński (2002) introduced Galois theory for corings with a fixed grouplike element. El Kaoutit and Gómez-Torrecillas (2003) generalized this to so-called comatrix corings. This establishes a general framework for existing Galois theories: classical Galois theory, Hopf-Galois theory, …

Oct. 18, 2023, 5:15 p.m.
MAGNUS B. LANDSTAD (Norges teknisk-naturvitenskapelige universitet, Trondheim, Norway)
EXOTIC GROUP ALGEBRAS, CROSSED PRODUCTS, AND COACTIONS
If G is a locally compact group, we have the full group C*-algebra C*(G) and the reduced C*_r(G). We call a C*-algebra properly between C*(G) and C*_r(G) exotic. Similarly, if G acts on a C*-algebra A we can form the full crossed product C*(GxA) and the …

Oct. 11, 2023, 5:15 p.m.
THERESE BASA LANDRY (University of California, Santa Barbara, USA)
SPECTRAL TRIPLES FOR NONCOMMUTATIVE SOLENOIDS
Noncommutative solenoids are inductive limit algebras built from rotation algebras. By viewing noncommutative solenoids as twisted group C*-algebras, we construct odd finitely summable spectral triples for noncommutative solenoids based on length functions of bounded doubling. …

Oct. 4, 2023, 5:15 p.m.
MANISH KUMAR (IMPAN, Warszawa, Poland)
FACTORIALITY AND FULLNESS OF q-ARAKI-WOODS VON NEUMANN ALGEBRAS
We discuss the factoriality, non-injectivity, and fullness questions of q-Araki-Woods von Neumann algebras, constructed by Hiai. These algebras are non-tracial counterparts of q-Gaussian algebras, which combine the q-deformations of free-group factors due to Bożejko, Kummerer and Speicher, and …

June 7, 2023, 5:15 p.m.
ROBERT YUNCKEN (Université Clermont Auvergne, France)
CRYSTALLIZING FUNCTIONS ON COMPACT LIE GROUPS
The theory of crystal bases, due to Kashiwara and Lusztig, is a means of simplifying the representation theory of semisimple Lie algebras by passing through quantum groups. Specifically, varying the parameter q of a quantized enveloping algebra, …