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Authors:
mak
Abstract: We establish convergence in norm and pointwise almost everywhere for the non-conventional (in the sense of Furstenberg) bilinear polynomial ergodic averages \[ A_N(f,g)(x) ≔ \frac{1}{N} \sum_{n =1}^N f(T^nx) g(T^{P(n)}x)\] as $N \to \infty$, where $T \colon X \to X$ is … Continue reading → PubDate: Fri, 21 Jan 2022 23:22:02 +000
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Authors:
mak
Abstract: For every abelian compact Lie group $A$, we prove that the homotopical $A$-equivariant complex bordism ring, introduced by tom Dieck (1970), is isomorphic to the $A$-equivariant Lazard ring, introduced by Cole–Greenlees–Kriz (2000). This settles a conjecture of Greenlees. We also … Continue reading → PubDate: Tue, 18 Jan 2022 20:15:27 +000
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Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
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Authors:
mak
Abstract: By means of M.A. Štan’ko’s clever unknotting technique we show that every embedding $f: M^{n-1} \to N^n (n\ge 5)$ from a topological $(n-1)$-manifold $M^{n-1}$ into a topological $n$-manifold $N^n$ can be approximated by locally flat embeddings. A serious technical difficulty … Continue reading → PubDate: Fri, 14 Jan 2022 02:13:09 +000
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Authors:
mak
Abstract: We give a negative answer to Ulam’s Problem 19 from the Scottish Book asking is a solid of uniform density which will float in water in every position a sphere' Assuming that the density of water is $1$, we show … Continue reading → PubDate: Mon, 10 Jan 2022 19:11:37 +000
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mak
Abstract: We prove a dimension formula for the weight-1 subspace of a vertex operator algebra $V^{\mathrm{orb}(g)}$ obtained by orbifolding a strongly rational, holomorphic vertex operator algebra $V$ of central charge 24 with a finite-order automorphism $g$. Based on an upper bound … Continue reading → PubDate: Wed, 29 Dec 2021 05:40:16 +000
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Authors:
annadmin
Abstract: This is an erratum for the paper “Stable intersections of regular Cantor sets with large Hausdorff dimensions” by Moreira and Yoccoz. We show how to fix a flaw — a bad choice of parameters — in the proof of the … Continue reading → PubDate: Wed, 29 Dec 2021 05:17:00 +000
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annadmin
Abstract: We prove the rank 1 case of a conjecture of Frenkel-Gaitsgory: critical level Kac-Moody representations with regular central characters localize onto the affine Grassmannian. The method uses an analogue in local geometric Langlands of the existence of Whittaker models for … Continue reading → PubDate: Wed, 29 Dec 2021 05:16:00 +000
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annadmin
Abstract: Original article: https://doi.org/10.4007/annals.2020.191.1.3 PubDate: Wed, 29 Dec 2021 05:15:00 +000
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annadmin
Abstract: We prove that all maximal-tb positive Legendrian torus links $(n,m)$ in the standard contact 3-sphere, except for $(2,m)$, $(3,3),(3,4)$ and $(3,5)$, admit infinitely many Lagrangian fillings in the standard symplectic \hbox 4-ball. This is proven by constructing infinite order Lagrangian … Continue reading → PubDate: Wed, 29 Dec 2021 05:13:00 +000
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annadmin
Abstract: We establish the Gaussian Multi-Bubble Conjecture: the least Gaussian-weighted perimeter way to decompose $\mathbb {R}^n$ into $q$ cells of prescribed (positive) Gaussian measure when $2 \leq q \leq n+1$, is to use a “simplicial cluster,” obtained from the Voronoi cells … Continue reading → PubDate: Wed, 29 Dec 2021 05:12:00 +000
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annadmin
Abstract: We construct Feigenbaum quadratic-like maps with a Julia set of positive Lebesgue measure. Indeed, in the quadratic family $P_c: z \mapsto z^2+c$ the corresponding set of parameters $c$ is shown to have positive Hausdorff dimension. Our examples include renormalization fixed … Continue reading → PubDate: Wed, 29 Dec 2021 05:12:00 +000
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Authors:
mak
Abstract: In this paper, we provide a new proof of the stable Adams conjecture. Our proof constructs a canonical null-homotopy of the stable J-homomorphism composed with a virtual Adams operation, by applying the $\mathrm{K}$-theory functor to a multinatural transformation. We also … Continue reading → PubDate: Sun, 19 Dec 2021 03:59:01 +000
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Authors:
mak
Abstract: We give a construction which produces irreducible complex rigid local systems on $\Bbb{P}_{\Bbb{C}}^1-\{p_1,\dots,p_s\}$ via quantum Schubert calculus and strange duality. These local systems are unitary and arise from a study of vertices in the polytopes controlling the multiplicative eigenvalue problem … Continue reading → PubDate: Mon, 06 Dec 2021 21:27:02 +000
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Authors:
mak
Abstract: We establish the satisfiability threshold for random k-SAT for all $k\ge k_0$, with $k_0$ an absolute constant. That is, there exists a limiting density $\alpha_{\mathrm{SAT}}(k)$ such that a random k-SAT formula of clause density $\alpha$ is with high probability satisfiable … Continue reading → PubDate: Thu, 02 Dec 2021 21:32:29 +000
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Authors:
mak
Abstract: We prove almost Lipshitz continuity of spectra of singular quasiperiodic Jacobi matrices and obtain a representation of the critical almost Mathieu family that has a singularity. This allows us to prove that the Hausdorff dimension of its spectrum is not … Continue reading → PubDate: Tue, 19 Oct 2021 02:29:21 +000
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Authors:
mak
Abstract: We show that $C^\infty$ surface diffeomorphisms with positive topological entropy have at most finitely many ergodic measures of maximal entropy in general, and at most one in the topologically transitive case. This answers a question of Newhouse, who proved that … Continue reading → PubDate: Tue, 12 Oct 2021 22:18:35 +000
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Authors:
mak
Abstract: We develop techniques of mimicking the Frobenius action in the study of universal homeomorphisms in mixed characteristic. As a consequence, we show a mixed characteristic Keel’s base point free theorem obtaining applications towards the mixed characteristic Minimal Model Program, we … Continue reading → PubDate: Thu, 07 Oct 2021 15:12:59 +000
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Authors:
mak
Abstract: We define the Chow $t$-structure on the $\infty$-category of motivic spectra $\mathcal{S}\mathcal{H}(k)$ over an arbitrary base field $k$. We identify the heart of this $t$-structure $\mathcal{S}\mathcal{H}(k)^{c\heartsuit}$ when the exponential characteristic of $k$ is inverted. Restricting to the cellular subcategory, we … Continue reading → PubDate: Thu, 07 Oct 2021 15:10:25 +000
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Authors:
mak
Abstract: We prove the local-in-time well-posedness for the solution of the compressible Euler equations in $3$-D, for the Cauchy data of the velocity, density and vorticity $(v,\varrho, \mathscr{w}) \in H^s\times H^s\times H^{s’}$, $2 < s'< s$. The result extends the sharp … Continue reading → PubDate: Tue, 05 Oct 2021 00:21:58 +000
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Authors:
mak
Abstract: Using an integral inequality, contributions are made towards the solutions of two long open problems. The first one concerns the determination of the best constant $C(p)$ in Bernstein’s inequality \[ \int_0^{2\pi} |H_n'(t)|^p dt \leqq C(p)n^p \int_0^{2\pi} |H_n(t)|^p dt, \qquad 0 … Continue reading → PubDate: Sat, 10 Jul 2021 03:39:55 +000
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Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
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