Tootfinder

Slices of the special linear algebraic cobordism spectrum
Ahina Nandy, Oliver R\"ondigs, Egor Zolotarev
https://arxiv.org/abs/2606.05020 https://arxiv.org/pdf/2606.05020 https://arxiv.org/html/2606.05020
arXiv:2606.05020v1 Announce Type: new
Abstract: Let $F$ be a field of exponential characteristic $e$. We compute the slices of $\mathbf{MSL}[e^{-1}]$, where $\mathbf{MSL}$ is the special linear algebraic cobordism spectrum defined by Panin and Walter. The answer is expressed in terms of the second page of the Adams-Novikov spectral sequence for the special unitary cobordism spectrum, which was explicitly determined by Novikov. Its applicability is demonstrated by computations with the slice spectral sequence for $\mathbf{MSL}$, which determine the first few Milnor-Witt stems of its homotopy groups (up to the third) in terms of very effective hermitian $K$-theory. We also establish a decomposition of the rational special linear algebraic cobordism spectrum over an arbitrary qcqs scheme.
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I would always assume without much thought that rational thinking and rational acting would always win in 'in the long run'.
That's the idea of enlightenment: There is a truth and we find it and act upon it in our best interest and mathematical optimization and so on.
But no. Also the success of rationality is dependent on society! It needs an environment to succeed.
Stupid example: If the police would punch everybody who makes rational arguments in public, people would abandon rationality.

New arXiv preprint!  With my #PurdueFortWayne colleague Yifei Pan.  🐘 Here's a thread (1/n)
https://arxiv.org/abs/2606.01447

Constructing Discontinuous but Locally Bounded Rational Functions using Łojasiewicz Inequalities
For real multivariate polynomials $P$ and $Q$ both vanishing at a point, if the zero set of $Q$ is contained in the zero set of $P$, then there exists a rational function of the form $P^{p}/Q^{q}$ which is locally bounded and such that its extension that vanishes on the zero set of $Q$ is discontinuous. The proof uses inequalities of Lojasiewicz.

Tip-functionalized gold nanorod micropillar arrays for millisecond-resolved photothermal neuromodulation toward retinal prosthetic applications https://advanced.onlinelibrary.wiley.com/doi/10.1002/adhm.202505652 retinal implant

#FLOSS ecosystem.
I don't think we have a clear idea yet of what's to come, but a recurring image in our conversations is that of feudal age alchemists: closed, hermetic, underground groups, sharing knowledge in tight secret circles, never with the wide public... it's certainly not a pretty picture, but it might be the "rational" conclusion for many.
When we see the threat of big corporations (or just petty unimaginative people) stealing our work, what can we do, when collective action has been labelled as criminal activity, other than hide or risk the severe consequences of being combative?
#ai #generativeAI #fuck_ai