4
votes
1answer
397 views
failure of $\square(\kappa)$ at an inaccessible $\kappa$
How can we force the failure of $\square(\kappa)$ at an inaccessible $\kappa$, where
$\square(\kappa)$ is defined as follows: There is a sequence $(C_i:i< \kappa)$ such that:
…
0
votes
0answers
194 views
Minimum count of linear dependent columns in tensor product
Good day!
I have a Vandermonde-like matrix $V = \left( \begin{array}{ccccc} 1 & \alpha & \alpha^2 & \ldots & \alpha^{n-1} \newline 1 & \alpha^2 & \alpha^4 …
asked Apr 16 2011 at 8:08
spk
10
votes
2answers
1k views
Stokes' theorem etc., for non-Hausdorff manifolds
This question is prompted by another one.
I want to motivate the definition of a scheme for people who know about manifolds(smooth, or complex analytic). So I define a manifold i …
2
votes
2answers
535 views
Application of coordinate-stretching transformation for Perfectly Matched Layer
A Perfectly Matched Layer (PML) is an absorbing boundary condition (ABC) which can be used to approximate free-field conditions for the numerical solution of wave equation problems …
8
votes
2answers
883 views
What is the infinite-dimensional-manifold structure on the space of smooth paths mod thin homotopy?
This question is motivated by the recent paper An invitation to higher gauge theory by Baez and Huerta, and the 2007 paper Parallel Transport and Functors by Schreiber and Waldorf. …
7
votes
1answer
509 views
Lower bound on # of nonzero digits in ternary expansions of powers of 2?
Does anyone know of any lower bounds on the number of nonzero digits that appear in powers of 2 when written to base 3? (Other than the easy "If it's more than 8 it has to have at …
16
votes
4answers
1k views
Spectrum of the Grothendieck ring of varieties
Here's a problem that may ultimately require just simple algebraic-geometry skills to be solved, or perhaps it's very deep and will never be solved at all. From the comments, some …
12
votes
2answers
844 views
topological “milnor’s conjecture” on torus knots.
Here's a question that has come up in a couple of talks that I have given recently.
The 'classical' way to show that there is a knot $K$ that is locally-flat slice in the 4-ball b …
2
votes
2answers
212 views
linear ordering of color balls
Suppose that $n+m$ balls of which $n$ are red and $m$ are blue, are arranged in a linear order, we know there are $(n+m)!$ possible orderings. If all red balls are alike and all bl …
7
votes
2answers
290 views
Generalization of the club filter
If $\alpha$ is a (limit) ordinal, then a subset $S\subseteq\alpha$ is club if $\alpha$ is closed as a subset of $\alpha$ under the order topology and unbounded in $\alpha$. The set …
6
votes
3answers
2k views
Simultaneous diagonalization
I'm pretty sure that the following (if true) is a standard result in linear algebra but unfortunately I could not find it anywhere and even worse I'm too dumb to prove it: Let $k$ …
5
votes
1answer
493 views
How can we show the spaces $M_{g}(n)$ and $M_{g, n}$ are homotopy equivalent?
How can we prove that the moduli space,$M_{g}(n)$, of genus $g$ Riemann surface with $n$ boundary components is homotopy equivalent to $M_{g,n}$, that is ,the moduli space of genus …
9
votes
2answers
978 views
Is there triangulated category version of Barr-Beck’s theorem?
It is well known that Beck's theorem for Comonad is equivalent to Grothendieck flat descent theory on scheme.
There are several version of derived noncommutative geometry. I wond …
6
votes
4answers
957 views
alternative construction of the quotient group
The background for this question is that I know that many students starting to learn algebra focus on the standard construction of the quotient group $G/N$ instead of working with …
0
votes
1answer
269 views
Convex sets and projections
Hello!
I recently started (it's purely self-education) reading a "Mathematical programming and optimizations" book, did a vast part of the exercises related to the theoretical par …
