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In Link, Witten claims (p. 54) that to quantize the moduli space of flat $SL(2,\mathbb{C})$ connections on a torus, one can simply quantize the cotangent bundle of a real torus and take the part invar …

$\DeclareMathOperator\B{B}\DeclareMathOperator\SU{SU}$Given a principal $E_8$ bundle $P\rightarrow X$ one can take the adjoint representation $\rho :E_8\rightarrow \SU(\mathbb C^{248})$ and form the a …

I have a question concering the family of Pellian equations $$x^2 - (k^2+1)y^2 = k^2. \qquad (*)$$ For an integer $k\geq 2$, the equation (*) has at least three classes of solutions in integers, c …

It seems to me that for most of the twentieth century, axiomatic foundations for mathematical theories were constructed with the (mostly allied) goals of minimizing the number of primitive notions and …

Let $X$ be an inner metric space with curvature bounded from below by $k$ in the sense of Toponogov. $\Sigma_p$ be the space of directions at point $p$. In the note by Plaut "Metric spaces of curvatur …

Recently I have met an interesting problem $\rho$: $G \rightarrow SL(2,R)$ be a faithful representions of a finite group by real 2\times 2 matrices of determinant 1, then we can get this group is cyli …

Given a nonsingular, projective variety $X$ of dimension $n$ over an algebraically closed field $k$. Over $k=\mathbb{C}$, the top chern class $c_n(T_X)$ of the tangent sheaf is the Euler characterist …

I know of two places where $K_{*}(\mathbb{Z}\pi_{1}(X))$ (the algebraic $K$-theory of the group ring of the fundamental group) makes an appearance in algebraic topology. The first is the Wall finit …

The Mazur-Ulam theorem says that any surjective isometry of normed vector spaces is affine. This argument doesn't seem to apply to Minkowski space (of special relativity) since the metric is indefinit …

No one's answered the question cumulant problem so here's a simpler question: Has anyone described or catalogued all sets of non-negative real numbers that are closed under addition? In particular, h …

It is well-known that for each planar graph, the number of paths from each source to each sink will give rise to a totally non-negative matrix. However, did anyone ever come up with a planar network w …

I have taken two introductory courses on logic. One was an undergraduate level and the second one was at the graduate level. Both used a set of notes written by the instructor. I'm thinking about grad …

I have a group of cohomological dimension 2 generated by two elements. Is it possible to deduce that the group is commutative or, more generally, does $\mathrm{cd}\ G=2$ imply anything about the relat …

In a thread in MSE I proposed an older routine of mine for the efficient computation of coefficients; I use a very similar routine for the quick&dirty computation of the Stieltjes-constants. This …

A coherent sheaf $\mathcal{F}$ over a Noetherian scheme $X$ is called (maximal) Cohen-Macaulay if $depth_{\mathcal{O}_x}(\mathcal{F}_x) = \dim\mathcal{O}_x$ for any $x\in X$, where $\mathcal{O}_x$ is …