At the end of a conference given by Alain Connes in 2000 (here is a video in French), a member of the audience asked a question. I transcribed and translated it for you below: A …

In the equivariant Atiyah-Singer index theorem, when $G$ is a compact group acting on a manifold $M$ and $R(G)$ is the representation ring of $G$. We have the analytic index $$ \te …

I am a Ph.D student involved in topics like integrability of foliations arising from center stable bundles of partially hyperbolic dynamical systems. These are generally only conti …

how to define the gradient of the scalar function on c* algebra when we treat the c* algebra from different view points: 1.c* algebra as a point on noncommutative-geometry. (cones …

In learning about the K-theory of $C^*$-algebras, I have encountered the following 3 proofs of Bott periodicity: $\bullet$ An argument based on Moyal quantization found in "Elemen …

I recently came across noncommutative geometry and found it rather interesting. I should mention that I'm a graduate student considering options for my research and if I were to na …

Does anyone know of a good, complete reference for non-commutative formal group laws (i.e. construction of a "Lazard ring," discussion of non-commutative formal groups, perhaps som …

The Woronowicz definition of a differential calculus over an algebra consists of a pair $(\Omega,$d$)$, where $\Omega$ is an $A-A$-bimodule, and $$ \text{d}:A \to \Omega, $$ is a …

I do not know whether it is a good place to ask this question or not. I want to PhD in operator algebras and non-commutative geometry. What are the best places in the world for t …

About 20 years ago I read in textbook that "all irreducible representations of compact groups are finite-dimensional", but me and the proof of this fact never met each other :) …

It seems that the current state of quantum Brownian motion is ill-defined. The best survey I can find is this one by László Erdös, but the closest the quantum Brownian motion comes …

I'm interested in the following construction. Start with derived category of coherent sheaves witch equivalent to derived category of representations of some dg-algebra. Quasi-iso …

I know that lots of effort is being put into quantization of geometry(NCG).This effort of course comes with the idea of operator algebra being a powerful machinery. Has any effort …

Consider the usual sphere $S^{n-1}\subset\mathbb R^n$. By Stone-Weierstrass $C(S^{n-1})$ is generated by the standard coordinates $x_1,\ldots,x_n:\mathbb R^n\to\mathbb R$, and in f …

I am looking for an example of computation of the isomorphism classes of $n$-point modules over a non-commutative generated graded algebra (assuming all good properties such as Noe …