North Atlantic Noncommutative Geometry Seminar

Jan. 13, 2021, 5:15 p.m.
TOMASZ BRZEZIŃSKI (Prifysgol Abertawe)
ENTER TRUSS
The talk introduces trusses, i.e. algebraic systems each consisting of a set with a ternary operation (making it into an abelian heap) and an associative binary operation distributing over the ternary one. We begin by explaining …

Dec. 16, 2020, 5:15 p.m.
WOJCIECH SZYMAŃSKI (Syddansk Universitet)
ON NONCOMMUTATIVE FIBRE BUNDLES
We discuss an algebraic framework for noncommutative fibre bundles with homogeneous spaces as typical fibres. We illustrate the general scheme with two examples, the flag manifold of the quantum SU(3) group and the quantum twistor bundle. Both examples are …

Dec. 9, 2020, 5:15 p.m.
XIAO HAN (IMPAN)
ON HOPF-GALOIS EXTENSIONS AND THE GAUGE GROUP OF GALOIS OBJECTS
For starters, we will recall the fundamental concept of a Hopf-Galois extension, and instantiate it through quantum principal SU(2)-bundles with noncommutative seven-spheres as total spaces and noncommutative four-spheres as base spaces. Then we will recall the construction …

Dec. 2, 2020, 5:15 p.m.
FRANCESCO D'ANDREA (Università degli Studi di Napoli Federico II)
ON THE NOTION OF A NONCOMMUTATIVE SUBMANIFOLD
T. Masson, motivated by the derivation-based differential calculus of M. Dubois-Violette and P. W. Michor, introduced in the 90's the notion of a submanifold algebra as a way to extend to the noncommutative realm the concept of a closed embedded submanifold of a …

Nov. 25, 2020, 5:15 p.m.
CHRISTIAN VOIGT (University of Glasgow)
QUANTUM CUNTZ-KRIEGER ALGEBRAS
The notion of a quantum graph, a concept going back to the work of Erdos-Katavolos-Shulman and Weaver, provides a noncommutative generalisation of finite graphs. Quantum graphs play an intriguing role in the analysis of quantum …

Nov. 18, 2020, 5:15 p.m.
ALEXANDER FREI (Københavns Universitet)
THE GAUGE-INVARIANT UNIQUENESS THEOREMFOR RELATIVE CUNTZ-PIMSNER ALGEBRAS
We present a new proof of the gauge-invariant uniqueness theorem for C*-correspondences that is conceptual and simplifies earlier arguments. The proof is based on a reasoning due to Evgenios Kakariadis, and treats all relative Cuntz-Pimsner algebras on equal footing. As a consequence, in …

Nov. 4, 2020, 5:15 p.m.
MARIUSZ TOBOLSKI (Uniwersytet Wrocławski)
THE BORSUK-ULAM THEOREM FOR LOCALLY TRIVIAL COMPACT G-SPACES
The Borsuk-Ulam-type conjecture of Baum, Dąbrowski, and Hajac states that, given a free action of a non-trivial compact Hausdorff group G on a compact Hausdorff space X, there is no continuous G-equivariant map from the join X*G to X. The goal of this talk is to explain …

Oct. 28, 2020, 5:15 p.m.
DEVARSHI MUKHERJEE (Universität Göttingen)
ANALYTIC CYCLIC HOMOLOGY IN POSITIVE CHARACTERISTIC
We define a homology theory for complete torsion-free bornological algebras over a complete discrete valuation ring. The theory satisfies homotopy invariance, Morita invariance and excision. We use these properties to compute our theory for Leavitt path algebras. For …

Oct. 21, 2020, 5:15 p.m.
JACEK KRAJCZOK (IMPAN)
COAMENABILITY OF TYPE-I LOCALLY COMPACT QUANTUM GROUPS VIA CONVOLUTION OPERATORS
We say that a locally compact quantum group is type I if its universal C*-algebra (which is the universal version of the C*-algebra of continuous functions vanishing at infinity on the dual quantum group) is type I. This class of quantum groups can be thought of as an intermediate …