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The scale of Schatten-von Neumann classes is noncommutatitve analog of classical $\ell_p$-spaces. A lot of researchers devoted their lives to study Banach geometric structure of these spaces. Differen …

In this question which I flag it as a community wiki, I search for a big list of $C^{*}$ algebras(and a big list of criterions) which do not admit a non trivial idempotent $C^{*}-$morphism. I kno …

The "injective continuum function hypothesis" (ICF) is the following statement. ICF (Version 0). For all cardinal numbers $\kappa$ and $\nu$, we have $2^\kappa = 2^\nu \rightarrow \kappa = \nu.$ …

The question is pretty much contained in the title: What are examples of equivalence relations of topological spaces which are neither stronger nor weaker than homotopy equivalence? Something that …

As everyone knows :P, a graph is a CW-complex of dimension 1. Knowing that, are there any interesting results in graph theory that arise from working with CW-complexes? And more specifically, in algor …

I am just wondering why Mathematics is often defined as The study of Structures, Logic and Numbers which I can concur with but still retain various questions in mind. I am a postgraduate student of F …

One of the main reasons I only supervised one PhD student is that I find it hard to find an appropriate topic for a PhD project. A good approach, in my view, is to have on the one hand a list of inter …

How does one introduce, or how were you introduced to characteristic classes? You can assume that the student is comfortable with principal bundles and connections on principal bundles. I am not as …

What tools are out there for creating mathematical illustrations in a what-you-see-is-what-you-get mode? Having struggled with tikz for several years, I've found creating figures in Omnigraffle (http …

Mathematics is written one-dimensionally, using symbols that make sense when put together on a line. The 2d sheets of paper that we use don't have enough room to write mathematics two-dimensionally. A …

The notion of beauty has historically led many mathematicians to fruitful work. Yet, I have yet to find a mathematical text which has attempted to elucidate what exactly makes certain geometric figure …

I am seeking "quotable equivalents" for MA (Martin's axiom). For the continuum hypothesis, examples of such statements are as follows. (a) (Sierpinski) The (xy) plane can be covered by countably many …

I know a couple of answers to the above question: They can be used for point counting over finite fields/estimating the distribution of primes in characteristic 0. There are various conjectures/resu …

I’m working on a paper that makes heavy use of colorful diagrams to supplement the text. For most of these it would probably not be possible to create grayscale versions that convey the same informati …

I am a PhD student at one university and an invited professor at a second, i.e. I do not have a permanent position in the second one. Now I need to indicate an affiliation in a journal paper but I do …