Tootfinder

This https://arxiv.org/abs/2306.12263 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Local Statistics in Normal Matrix Models with Merging Singularity
We study the normal matrix model, also known as the two-dimensional one-component plasma at a specific temperature, with merging singularity. As the number $n$ of particles tends to infinity we obtain the limiting local correlation kernel at the singularity, which is related to the parametrix of the Painlevé~II equation. The two main tools are Riemann-Hilbert problems and the generalized Christoffel-Darboux identity. The correlation kernel exhibits a novel anisotropic scaling behavior, where t…

This https://arxiv.org/abs/2401.10771 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Study of Orbital Dynamics in Singular and Regular Naked Singularity Space-times
The universe is filled with various compact objects and the most attractive of them are the black holes and singularity. But it is also known that at the singularity density becomes so infinitely high that the present physics knowledge breaks down. Thus, the singularity remains a flaw of the present theories. Several methods have been exercised to resolve the singularity. One such mathematical method is through conformal transformations. This paper deals with regularizing a naked singularity sp…

This https://arxiv.org/abs/2401.10771 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Study of Orbital Dynamics in Singular and Regular Naked Singularity Space-times
The universe is filled with various compact objects and the most attractive of them are the black holes and singularity. But it is also known that at the singularity density becomes so infinitely high that the present physics knowledge breaks down. Thus, the singularity remains a flaw of the present theories. Several methods have been exercised to resolve the singularity. One such mathematical method is through conformal transformations. This paper deals with regularizing a naked singularity sp…

Mutual singularity of Riesz products on the unit sphere
Evgueni Doubtsov
https://arxiv.org/abs/2404.02652 https://arxiv.org/pdf/2404.…

Mutual singularity of Riesz products on the unit sphere
We prove analogs of Peyrière's mutual singularity theorem for standard and generalized Riesz products on the unit sphere of $\mathbb{C}^n$, $n\ge 2$. As a corollary, we obtain an analog of Zygmund's dichotomy for the Riesz products under consideration.

Oscillatory free boundary problems in stochastic materials
Dami\~ao J. Ara\'ujo, Ginaldo S. S\'a, Eduardo V. Teixeira, Jos\'e Miguel Urbano
https://arxiv.org/abs/2404.03060

Oscillatory free boundary problems in stochastic materials
We investigate a class of free boundary problems with oscillatory singularities within stochastic materials. Our main result yields sharp regularity estimates along the free boundary, provided the power of the singularity varies in a Dini-continuous fashion below a certain threshold. We also reveal an interesting repelling estimate preventing the free boundary from touching the region where the singularity power oscillates above the threshold.

This https://arxiv.org/abs/2402.06017 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Deformations of Zappatic stable surfaces and their Galois covers
This paper has an appendix, written by considers some algebraic surfaces that can deform to planar Zappatic stable surfaces with a unique singularity of type En. We prove that the Galois covers of these surfaces are all simply connected of general type, for n>=4, and we give a formula for Chern numbers of such Galois covers. As an application, we prove that such surfaces do not exist for n>30. Furthermore, Kollar improves the result to n>9 in Appendix 5.

The Social Media Sameness Singularity (Smith, 2016) continues.
https://www.theverge.com/2024/4/3/24119721/facebook-updated-full-screen-video-player-vertical-view

Facebook’s new full-screen video player looks a lot like TikTok
The platform’s update will feature vertical videos by default, bringing the full-screen, vertically oriented look to Reels, Facebook Live, and longform videos.

This https://arxiv.org/abs/2309.08917 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

On the UV/IR mixing of Lie algebra-type noncommutatitive $ϕ^4$-theories
We show that a UV divergence of the propagator integral implies the divergences of the UV/IR mixing in the two-point function at one-loop for a $ϕ^4$-theory on a generic Lie algebra-type noncommutative space-time. The UV/IR mixing is defined as a UV divergence of the planar contribution and an IR singularity of the non-planar contribution, the latter being due to the former UV divergence, and the UV finiteness of the non-planar contribution. Some properties of this general treatment are discus…

On coincidences of singular loci of types $\Sigma^{1_r}$ and $\Sigma^r$
Andr\'as Cs\'epai, Andr\'as Sz\H{u}cs, Tam\'as Terpai
https://arxiv.org/abs/2403.00332

On coincidences of singular loci of types $Σ^{1_r}$ and $Σ^r$
It is well-known that the Thom polynomial in Stiefel--Whitney classes expressing the cohomology class dual to the locus of the cusp singularity for codimension-$k$ maps $Σ^{1_2}(k)$ and that of the corank-$2$ singularity for codimension-$(k-1)$ maps $Σ^2(k-1)$ coincide: both are $w_{k+1}^2 + w_k w_{k+2}$. The aim of the present paper is to find out whether there is any geometric explanation to this seemingly mysterious coincidence. We thank László Fehér for posing us this interesting quest…

This https://arxiv.org/abs/2204.07007 has been replaced.
link: https://scholar.google.com/scholar?q=a

Symplectic monodromy at radius zero and equimultiplicity of $μ$-constant families
We show that every family of isolated hypersurface singularity with constant Milnor number has constant multiplicity. To achieve this, we endow the A'Campo model of "radius zero" monodromy with a symplectic structure. This new approach allows to generalize a spectral sequence of McLean converging to fixed point Floer homology of iterates of the monodromy to a more general setting which is well suited to study $μ$-constant families.