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Score of 0
0 answers
27 views

Gardam [1] disproved the Kaplansky unit conjecture by exhibiting a nontrivial unit $\alpha$ of support size 21 in $\mathbb{F}_2[P]$, where $P = \langle a,b \mid b^{-1}a^2b = a^{-2},\ a^{-1}b^2a = b^{-...
Score of 7
1 answer
415 views

So as you may know, the Jacobian conjecture turned out to be false for polynomials in three or more variables. It holds in one variable, but the simplest non trivial case is that of two variables. Are ...
Score of 5
0 answers
81 views

Let $R$ be a two-sided noetherian ring (not necessarily commutative). Question: Is there a bijection between the simple left $R$- modules and the simple right $R$-modules? One might ask further ...
Score of 2
0 answers
80 views

There are examples of matroids which can be represented by real vectors but cannot be represented by rational vectors. One such example is the Perles matroid, which cannot be represented over $\mathbb{...
Score of 2
0 answers
20 views

Let $k$ be a non-negative integer and $\gamma \in (0,1]$, so that for $s = k+\gamma$, the Zygmund space is $$C^s(\mathbb T^d):= C^{k,\gamma}(\mathbb T^d).$$ The norm on this space is any one which is ...
Score of -1
0 answers
28 views

I am investigating a split-operator framework for the 3D incompressible Navier–Stokes equations under the decomposition $u = U_L + v$, where $u_{0,L} \in H^2 \cap L^3$ and the critical perturbation ...
Score of 1
0 answers
20 views

Let $X$ be a homogeneous space $G/P$ and consider the moduli space $\overline{M}_{0,3}(X,d)$ for an arbitrary degree $d$. Let $f$ be a generic curve of degree $d$. We have one trivial bound on the ...
Score of 1
0 answers
18 views

I am studying a Monte Carlo method for the heat equation with Neumann boundary conditions. For a half-space, the Neumann heat kernel is given exactly by the method of images, $$G_N(x,y,t) =G(x-y,t)+G(...
Score of 3
0 answers
35 views

For real $r_1,r_2$ and $\kappa=\tfrac14$, is there a closed form for $$ \mathcal M(s)\;=\;\int_0^\infty W_{\kappa,\,i r_1}(x)\,W_{\kappa,\,i r_2}(x)\,x^{s-1}\,dx, $$ where $W_{\kappa,\mu}$ is the ...
Score of 4
0 answers
54 views

Let $L$ be a CW complex with $\pi_n(L) = 0$ for $n\geq3$ and vanishing $k$-invariant. Write $\pi$ for the fundamental group and $A$ for $\pi_2(L)$ as a $\mathbb{Z}\pi$-module. The vanishing $k$-...
Score of 3
0 answers
127 views

Usually this would be the kind of question that will raise eyebrows as to its appropriateness to this site, but after talking to several colleagues offline and online, it seems that it is indeed ...
Score of 2
0 answers
3479 views

Sorry if this is not the correct place to ask this question, or if this is somewhat vague, but it should be well-known by now that the Jacobian Conjecture has been disproven with a surprisingly simple ...
Score of 6
1 answer
143 views

I'm not sure if my question is appropriate here so please redirect me if I should post on StackExchange instead. Is there a resource (likelier to be paper than book) that discusses the specific ...
Score of -6
1 answer
609 views

Yesterday (Jul 19) Levent Alpoge announced a polynomial map $F:\mathbb C^3\to\mathbb C^3$ with $\det DF\equiv-2$ and a fiber containing three distinct points: a noninjective Keller map in dimension $3$...
Score of 4
0 answers
2324 views

Background Yesterday (July 19, 2026) Levent Alpöge tweeted (source) the polynomial map $F=(a,b,c):\mathbb{C}^3\to\mathbb{C}^3$, \begin{align*} a&=(1+xy)^3z+y^2(1+xy)(4+3xy),\\ b&=y+3x(1+xy)^2z+...

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