North Atlantic Noncommutative Geometry Seminar

Jan. 11, 2023, 5:15 p.m.
AHMAD REZA HAJ SAEEDI SADEGH (Northeastern University)
DEFORMATION SPACES, GETZLER'S RESCALING, AND AN EQUIVARIANT INDEX THEOREM FOR LIE GROUPOIDS
In recent work, Higson and Yi developed a new perspective on Getzler's symbol calculus, reinterpreting the latter in terms of a convolution algebra of sections of the rescaled bundle over the tangent groupoid of a spin manifold. …

Dec. 21, 2022, 5:15 p.m.
MARIUSZ TOBOLSKI (Uniwersytet Wrocławski)
THE CONTRAVARIANT FUNCTORIALITY OF GRAPH ALGEBRAS
We introduce a subcategory of directed graphs for which the construction of Leavitt path algebras induces a contravariant functor into the category of algebras. Then we prove a theorem stating under which conditions this functor …

Dec. 14, 2022, 5:15 p.m.
JACEK KRAJCZOK (University of Glasgow)
APPROXIMATION PROPERTIES FOR LOCALLY COMPACT QUANTUM GROUPS
One of the most widely studied properties of groups is the notion of amenability. In one of its many formulations, it gives us a way of approximating constant functions by functions in the Fourier algebra. …

Dec. 7, 2022, 5:15 p.m.
JACK SPIELBERG (Arizona State University)
RELATIVE GRAPHS AND PULLBACKS OF RELATIVE TOEPLITZ GRAPH ALGEBRAS
We generalize a result from a recent paper of Hajac, Reznikoff and Tobolski. In that paper they give conditions they call "admissibility" on a pushout diagram in the category of directed graphs implying that the …

Nov. 30, 2022, 5:15 p.m.
MATTHIAS SCHÖTZ (IMPAN)
GELFAND-NAIMARK THEOREMS OF ORDERED *-ALGEBRAS
Ordered *-algebras (i.e. unital *-algebras endowed with a quadratic module of "positive" elements) provide an abstraction of *-algebras of possibly unbounded operators on Hilbert, or pre-Hilbert, spaces. In this sense, they are generalizations of C*-algebras …

Nov. 23, 2022, 5:15 p.m.
MARC A. RIEFFEL (UC Berkeley)
CONVERGENCE OF FOURIER TRUNCATIONS
We generalize the Fejer-Riesz operator systems defined for the circle group by Connes and van Suijlekom to the setting of compact matrix quantum groups and their ergodic actions on C*-algebras. These truncations form filtrations of …

Nov. 16, 2022, 5:15 p.m.
LUDWIK DĄBROWSKI (SISSA)
SPECTRAL METRIC AND EINSTEIN FUNCTIONALS
Using the Wodzicki residue, in terms of the Laplace operator, we define two bilinear functionals on vector fields. Their densities yield, respectively, the metric tensor and the Einstein tensor on an even-dimensional Riemannian manifold. Then, in terms of the Dirac …

Nov. 9, 2022, 5:15 p.m.
BRAM MESLAND (Universiteit Leiden)
CURVATURE FOR DIFFERENTIABLE HILBERT MODULES
In this talk, we introduce the curvature of densely defined universal connections on Hilbert C*-modules, relative to a spectral triple, leading to a well defined curvature operator. Algebraically, this curvature can be interpreted as the …

Nov. 2, 2022, 5:15 p.m.
SØREN EILERS (Københavns Universitet)
EQUIVARIANT ISOMORPHISMS OF QUANTUM LENS SPACES
Since their inception two decades ago, the quantum lens spaces of Hong and Szymański have been studied very successfully, due in no small part to the fact — established from the outset — that they …

Oct. 26, 2022, 5:15 p.m.
PIOTR M. HAJAC (IMPAN)
COUNTING PATHS IN DIRECTED GRAPHS
We consider the class of directed graphs with N edges and without loops shorter than k. Using the concept of a labelled graph and a recent result of Alexandru Chirvasitu, I will show how to determine graphs from …

Oct. 19, 2022, 5:15 p.m.
ALEXANDRU CHIRVASITU (SUNY Buffalo)
CENTERS AS UNIVERSAL GRADING GROUPS OF REPRESENTATION CATEGORIES
It is a result of Müger that, for a compact group G, associating to every irreducible G-representation its central character identifies the Pontryagin dual of the center Z(G) with the universal group that, in a certain sense, labels the grading of the …

Oct. 12, 2022, 5:15 p.m.
FRANCESCO D'ANDREA (Università degli Studi di Napoli Federico II)
THE CONVOLUTION ALGEBRA OF A TOLERANCE RELATION
It is well known that a "bad" quotient space can be studied by associating to it the groupoid C*-algebra of its defining equivalence relation. A similar procedure for relations that are reflexive and symmetric but fail to be transitive leads to …

Oct. 5, 2022, 5:15 p.m.
MARIUSZ TOBOLSKI (Uniwersytet Wrocławski)
THE STONE-VON NEUMANN THEOREM FOR LOCALLY COMPACT QUANTUM GROUPS
The Stone-von Neumann theorem rigorously shows the equivalence between two fundamental approaches to quantum mechanics, notably, the matrix mechanics of Heisenberg and the wave mechanics of Schrödinger. This theorem was formulated by Mackey as a …

June 15, 2022, 5:15 p.m.
HENRI MOSCOVICI (Ohio State University)
PROLATE SERENDIPITY AND THE ZEROS OF ZETA
This talk is about the joint work with Alain Connes in which we display an isospectral family of Dirac-type operators whose ultraviolet spectrum matches remarkably well the zeros of the Riemann zeta function.

June 8, 2022, 5:15 p.m.
PAULO CARRILLO ROUSE (Université Paul Sabatier, Toulouse III)
A DEFORMATION-GROUPOID APPROACH TO THE BAUM-CONNES ASSEMBLY MAP
In a recent preprint, together with Bai-Ling Wang and Hang Wang, following the ideas of Connes and Moscovici, we give an explicit formula (in terms of a pairing of forms and currents) for the pairing …