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Interpolation and duality in algebras of multipliers on the ball J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-04-26 Kenneth R. Davidson,Michael Hartz
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Effective joint equidistribution of primitive rational points on expanding horospheres J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-04-26 Daniel El-Baz,Bingrong Huang,Min Lee
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Measurable equidecompositions for group actions with an expansion property J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-04-26 Łukasz Grabowski,András Máthé,Oleg Pikhurko
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Nearby cycles and semipositivity in positive characteristic J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-04-26 Adrian Langer
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Nonuniqueness of minimizers for semilinear optimal control problems J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-04-13 Dario Pighin
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Commensurated subgroups and micro-supported actions (with an appendix by Dominik Francoeur) J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-04-13 Pierre-Emmanuel Caprace,Adrien Le Boudec
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The Riemannian quantitative isoperimetric inequality J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-04-13 Otis Chodosh,Max Engelstein,Luca Spolaor
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Deep learning via dynamical systems: An approximation perspective J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-04-13 Qianxiao Li,Ting Lin,Zuowei Shen
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Stationary $C^*$-dynamical systems (with an appendix by Uri Bader, Yair Hartman, and Mehrdad Kalantar) J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-04-13 Yair Hartman,Mehrdad Kalantar
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Splitting methods and short time existence for the master equations in mean field games J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-04-13 Pierre Cardaliaguet,Marco Cirant,Alessio Porretta
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Integral $p$-adic Hodge filtrations in low dimension and ramification J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-04-06 Shizhang Li
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Fourier uniqueness pairs of powers of integers J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-04-06 João P. G. Ramos,Mateus Sousa
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Heegaard Floer homology and cosmetic surgeries in $S^3$ J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-03-17 Jonathan Hanselman
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Fast optimization via inertial dynamics with closed-loop damping J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-03-16 Hedy Attouch,Radu Ioan Boţ,Ernö Robert Csetnek
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Lipschitz stratification of complex hypersurfaces in codimension 2 J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-03-14 Adam Parusiński,Laurenţiu Păunescu
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Strong nonlinear instability and growth of Sobolev norms near quasiperiodic finite gap tori for the 2D cubic NLS equation J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-03-02 Marcel Guardia,Zaher Hani,Emanuele Haus,Alberto Maspero,Michela Procesi
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Hodge–Tate decomposition for non-smooth spaces J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-03-02 Haoyang Guo
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Instabilities of invariant quasi-periodic tori J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-02-28 Gerard Farré,Bassam Fayad
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Systoles and Lagrangians of random complex algebraic hypersurfaces J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-02-28 Damien Gayet
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Chern classes in precobordism theories J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-02-22 Toni Annala
We construct Chern classes of vector bundles in the universal precobordism theory of Annala--Yokura over an arbitrary Noetherian base ring of finite Krull dimension. As an immediate corollary of this, we show that the Grothendieck ring of vector bundles can be recovered from the universal precobordism ring, and that we can construct candidates for Chow rings satisfying an analogue of the classical
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Does Leray’s structure theorem withstand buoyancy-driven chemotaxis-fluid interaction? J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-02-22 Michael Winkler
In a smoothly bounded convex domain Ω ⊂ R, we consider the chemotaxis-Navier-Stokes model nt + u · ∇n = ∆n−∇ · (n∇c), x ∈ Ω, t > 0, ct + u · ∇c = ∆c− nc, x ∈ Ω, t > 0, ut + (u · ∇)u = ∆u+∇P + n∇Φ, ∇ · u = 0, x ∈ Ω, t > 0, (⋆) proposed by Goldstein et al. to describe pattern formation in populations of aerobic bacteria interacting with their liquid environment via transport and buoyancy. Known
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The monodromy of generalized Kummer varieties and algebraic cycles on their intermediate Jacobians J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-02-22 Eyal Markman
We compute the subgroup of the monodromy group of a generalized Kummer variety associated to equivalences of derived categories of abelian surfaces. The result was previously announced in arXiv:1201.0031. Mongardi showed that the subgroup constructed here is in fact the whole monodromy group. As an application we prove the Hodge conjecture for the generic abelian fourfold of Weil type with complex
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Erratum to “Uniform K-stability and asymptotics of energy functionals in Kähler geometry” J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-01-13 Sébastien Boucksom, Tomoyuki Hisamoto, Mattias Jonsson
The goal of this note is to indicate a gap in the proof of Theorem 5.6 of [J. Eur. Math. Soc. 21, 2905–2944 (2019)], and the consequences it has on other results in the same paper. Let us stress that the main result (Theorem A), which expresses the slopes at infinity of functionals in algebro-geometric terms, is independent of the flawed result, and thus remains valid.
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On the largest prime factor of $n^2+1$ J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-02-04 Jori Merikoski
We show that the largest prime factor of $n^2+1$ is infinitely often greater than $n^{1.279}$. This improves the result of de la Bret\`eche and Drappeau (2019) who obtained this with $1.2182$ in place of $1.279.$ The main new ingredients in the proof are a new Type II estimate and using this estimate by applying Harman's sieve method. To prove the Type II estimate we use the bounds of Dehouillers and
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Smooth stationary water waves with exponentially localized vorticity J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-01-28 Mats Ehrnström,Samuel Walsh,Chongchun Zeng
We study stationary capillary-gravity waves in a two-dimensional body of water that rests above a flat ocean bed and below vacuum. This system is described by the Euler equations with a free surface. Our main result states that there exist large families of such waves that carry finite energy and exhibit an exponentially localized distribution of (nontrivial) vorticity. This is accomplished by combining
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On the Möbius function in all short intervals J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-01-28 Kaisa Matomäki,Joni Teräväinen
We show that, for the Mobius function $\mu(n)$, we have $$ \sum_{x 0.55$. This improves on a result of Ramachandra from 1976, which is valid for $\theta>7/12$. Ramachandra's result corresponded to Huxley's $7/12$ exponent for the prime number theorem in short intervals. The main new idea leading to the improvement is using Ramare's identity to extract a small prime factor from the $n$-sum. The proof
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Concordance surgery and the Ozsváth–Szabó 4-manifold invariant J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-01-28 András Juhász,Ian Zemke
We compute the effect of concordance surgery, a generalization of knot surgery defined using a self-concordance of a knot, on the Ozsv\'ath-Szab\'o 4-manifold invariant. The formula involves the graded Lefschetz number of the concordance map on knot Floer homology. The proof uses the sutured Floer TQFT, and a version of sutured Floer homology perturbed by a 2-form.
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An ultimate proof of Hoffmann–Totaro’s conjecture J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-01-28 Nikita Karpenko
We prove the last open case of the conjecture on the possible values of the first isotropy index of an anisotropic quadratic form over a field. It was initially stated by Detlev Hoffmann for fields of characteristic ̸= 2 and then extended to arbitrary characteristic by Burt Totaro. The initial statement was proven by the author in 2002. In characteristic 2, the case of a totally singular quadratic
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Lagrangian chaos and scalar advection in stochastic fluid mechanics J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-01-28 Jacob Bedrossian, Alex Blumenthal, Sam Punshon-Smith
We study the Lagrangian flow associated to velocity fields arising from various models of stochastic fluid mechanics. We prove that in many circumstances, these flows are chaotic, that is, the top Lyapunov exponent is strictly positive (almost surely, all particle trajectories are simultaneously exponentially sensitive with respect to initial conditions). Our main results are for the Navier–Stokes
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Semi-local simple connectedness of non-collapsing Ricci limit spaces J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-01-25 Jiayin Pan,Guofang Wei
Let $X$ be a non-collapsing Ricci limit space and let $x\in X$. We show that for any $\epsilon>0$, there is $r>0$ such that every loop in $B_t(x)$ is contractible in $B_{(1+\epsilon)t}(x)$, where $t\in(0,r]$. In particular, $X$ is semi-locally simply connected.
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Vanishing theorems for Shimura varieties at unipotent level J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-01-18 Ana Caraiani,Daniel R. Gulotta,Christian Johansson
We show that the compactly supported cohomology of Shimura varieties of Hodge type of infinite $\Gamma_1(p^\infty)$-level (defined with respect to a Borel subgroup) vanishes above the middle degree, under the assumption that the group of the Shimura datum splits at $p$. This generalizes and strengthens the vanishing result proved in "Shimura varieties at level $\Gamma_1(p^\infty)$ and Galois representations"
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An optimal transport formulation of the Einstein equations of general relativity J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-01-14 Andrea Mondino,Stefan Suhr
The goal of the paper is to give an optimal transport formulation of the full Einstein equations of general relativity, linking the (Ricci) curvature of a space-time with the cosmological constant and the energy-momentum tensor. Such an optimal transport formulation is in terms of convexity/concavity properties of the Shannon-Bolzmann entropy along curves of probability measures extremizing suitable
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Normality and Cohen–Macaulayness of parahoric local models J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-01-04 Thomas J. Haines,Timo Richarz
We study the singularities of integral models of Shimura varieties and moduli stacks of shtukas with parahoric level structure. More generally our results apply to the Pappas-Zhu and Levin mixed characteristic parahoric local models, and to their equal characteristic analogues. For any such local model we prove under minimal assumptions that the entire local model is normal with reduced special fiber
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Spectral multipliers and wave equation for sub-Laplacians: lower regularity bounds of Euclidean type J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-01-04 Alessio Martini,Detlef Müller,Sebastiano Nicolussi Golo
Let $\mathscr{L}$ be a smooth second-order real differential operator in divergence form on a manifold of dimension $n$. Under a bracket-generating condition, we show that the ranges of validity of spectral multiplier estimates of Mihlin--Hormander type and wave propagator estimates of Miyachi--Peral type for $\mathscr{L}$ cannot be wider than the corresponding ranges for the Laplace operator on $\mathbb{R}^n$
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Galois representations for general symplectic groups J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-01-04 Arno Kret,Sug Woo Shin
We prove the existence of GSpin-valued Galois representations corresponding to cohomological cuspidal automorphic representations of general symplectic groups over totally real number fields under the local hypothesis that there is a Steinberg component. This confirms the Buzzard-Gee conjecture on the global Langlands correspondence in new cases. As an application we complete the argument by Gross
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Ricci curvature in dimension 2 J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-01-04 Alexander Lytchak,Stephan Stadler
We prove that in two dimensions the synthetic notions of lower bounds on sectional and on Ricci curvature coincide.
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From non-defectivity to identifiability J. Eur. Math. Soc. (IF 2.6) Pub Date : 2022-01-04 Alex Casarotti,Massimiliano Mella
A projective variety $X\subset\mathbb{P}^N$ is $h$-identifiable if the generic element in its $h$-secant variety uniquely determines $h$ points on $X$. In this paper we propose an entirely new approach to study identifiability, connecting it to the notion of secant defect. In this way we are able to improve all known bounds on identifiability. In particular we give optimal bounds for some Segre and
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Variation of singular Kähler–Einstein metrics: Kodaira dimension zero J. Eur. Math. Soc. (IF 2.6) Pub Date : 2021-12-23 Junyan Cao,Henri Guenancia,Mihai Paun,Valentino Tosatti
We study several questions involving relative Ricci-flat Kahler metrics for families of log Calabi-Yau manifolds. Our main result states that if $p:(X,B)\to Y$ is a Kahler fiber space such that $\displaystyle (X_y, B|_{X_y})$ is generically klt, $K_{X/Y}+B$ is relatively trivial and $p_*(m(K_{X/Y}+B))$ is Hermitian flat for some suitable integer $m$, then $p$ is locally trivial. Motivated by questions
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On the structure of random graphs with constant $r$-balls J. Eur. Math. Soc. (IF 2.6) Pub Date : 2021-12-21 Itai Benjamini,David Ellis
We continue the study of the properties of graphs in which the ball of radius $r$ around each vertex induces a graph isomorphic to the ball of radius $r$ in some fixed vertex-transitive graph $F$, for various choices of $F$ and $r$. This is a natural extension of the study of regular graphs. More precisely, if $F$ is a vertex-transitive graph and $r \in \mathbb{N}$, we say a graph $G$ is {\em $r$-locally
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Optimal identification of cavities in the Generalized Plane Stress problem in linear elasticity J. Eur. Math. Soc. (IF 2.6) Pub Date : 2021-12-21 Antonino Morassi,Edi Rosset,Sergio Vessella
For the Generalized Plane Stress (GPS) problem in linear elasticity, we obtain an optimal stability estimate of logarithmic type for the inverse problem of determining smooth cavities inside a thin isotropic cylinder {}from a single boundary measurement of traction and displacement. The result is obtained by reformulating the GPS problem as a Kirchhoff-Love plate-like problem in terms of the Airy's
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Entire solutions to equations of minimal surface type in six dimensions J. Eur. Math. Soc. (IF 2.6) Pub Date : 2021-12-21 Connor Mooney
We construct nonlinear entire solutions in $\mathbb{R}^6$ to equations of minimal surface type that correspond to parametric elliptic functionals.
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Sharp stability of Brunn–Minkowski for homothetic regions J. Eur. Math. Soc. (IF 2.6) Pub Date : 2021-12-21 Peter van Hintum,Hunter Spink,Marius Tiba
The Brunn-Minkowski inequality applied to homothetic regions states that $|A| \le |tA+(1-t)A|$ for $A\subset \mathbb{R}^n$ and $t \in [0,1]$. We show there is a constant $C_n>0$ and constants $d_n(\tau)>0$ for each $\tau \in (0,\frac{1}{2}]$ such that if $t \in [\tau,1-\tau]$ and $|(tA+(1-t)A)\setminus A|\le d_n(\tau)|A|$, then $|co(A)\setminus A| \le C_n \tau^{-1}|(tA+(1-t)A)\setminus A|$, which is
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$p$-adic $L$-functions of Hilbert cusp forms and the trivial zero conjecture J. Eur. Math. Soc. (IF 2.6) Pub Date : 2021-12-21 Daniel Barrera, Mladen Dimitrov, Andrei Jorza
We prove a strong form of the trivial zero conjecture at the central point for the $p$-adic $L$-function of a non-critically refined self-dual cohomological cuspidal automorphic representation of $\operatorname{GL}_2$ over a totally real field, which is Iwahori spherical at places above $p$. In the case of a simple zero we adapt the approach of Greenberg and Stevens, based on the functional equation
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Circular flows for the Euler equations in two-dimensional annular domains, and related free boundary problems J. Eur. Math. Soc. (IF 2.6) Pub Date : 2021-12-08 François Hamel,Nikolai Nadirashvili
In this paper, we consider steady Euler flows in two-dimensional bounded annuli, as well as in exterior circular domains, in punctured disks and in the punctured plane. We always assume rigid wall boundary conditions. We prove that, if the flow does not have any stagnation point, and if it satisfies further conditions at infinity in the case of an exterior domain or at the center in the case of a punctured
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Regularity of the singular set in the fully nonlinear obstacle problem J. Eur. Math. Soc. (IF 2.6) Pub Date : 2021-12-08 Ovidiu Savin,Hui Yu
For the obstacle problem involving a convex fully nonlinear elliptic operator, we show that the singular set in the free boundary stratifies. The top stratum is locally covered by a $C^{1,\alpha}$-manifold, and the lower strata are covered by $C^{1,\log^\varepsilon}$-manifolds. This essentially recovers the regularity result obtained by Figalli-Serra when the operator is the Laplacian.
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Slope inequalities and a Miyaoka–Yau type inequality J. Eur. Math. Soc. (IF 2.6) Pub Date : 2021-12-08 Yi Gu,Xiaotao Sun,Mingshuo Zhou
We prove several slope inequalities for a relative minimal surface fibration in positive characteristic. As an application, we prove a Miyaoka-Yau type ineqaulity $\chi(\sO_S)\ge\frac{p^2-4p-1}{4(3p+1)(p-3)}K_S^2$ for all minimal surface $S$ of general type in characteristic $p\ge 5$ and the equality holds for Raynaud's examples. Some similar inequalities are also established for $p=2,3$, which answer
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Measure preserving diffeomorphisms of the torus are unclassifiable J. Eur. Math. Soc. (IF 2.6) Pub Date : 2021-12-08 Matthew Foreman, Benjamin Weiss
In 1932 von Neumann proposed classifying the statistical behavior of differentiable systems. In modern language this is interpreted as classifying diffeomorphisms of compact manifolds up to measure isomorphism. This paper proves that this is impossible in a rigorous sense.
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Local and global applications of the Minimal Model Program for co-rank 1 foliations on threefolds J. Eur. Math. Soc. (IF 2.6) Pub Date : 2021-12-07 Calum Spicer,Roberto Svaldi
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Coulomb branches of quiver gauge theories with symmetrizers J. Eur. Math. Soc. (IF 2.6) Pub Date : 2021-12-07 Hiraku Nakajima,Alex Weekes
We generalize the mathematical definition of Coulomb branches of $3$-dimensional $\mathcal N=4$ SUSY quiver gauge theories in arXiv:1503.03676, arXiv:1601.03686, arXiv:1604.03625 to the cases with symmetrizers. We obtain generalized affine Grassmannian slices of type $BCFG$ as examples of the construction, and their deformation quantizations via truncated shifted Yangians. Finally, we study modules
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Long range order in atomistic models for solids J. Eur. Math. Soc. (IF 2.6) Pub Date : 2021-11-19 Alessandro Giuliani, Florian Theil
The emergence of long range order at low temperatures in atomistic systems with continuous symmetry is a fundamental, yet poorly understood phenomenon in physics. To address this challenge we study a discrete microscopic model for an elastic crystal with dislocations in three dimensions, previously introduced by Ariza and Ortiz. The model is rich enough to support some realistic features of three-dimensional
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Local convergence of random planar graphs J. Eur. Math. Soc. (IF 2.6) Pub Date : 2021-11-17 Benedikt Stufler
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A cone restriction estimate using polynomial partitioning J. Eur. Math. Soc. (IF 2.6) Pub Date : 2021-11-17 Yumeng Ou, Hong Wang
We obtain an improved Fourier restriction estimate for a truncated cone using the method of polynomial partitioning in dimension $n\geq 3$, which in particular solves the cone restriction conjecture for $n=5$, and recovers the sharp range for $3\leq n\leq 4$. The main ingredient of the proof is a $k$-broad estimate for the cone extension operator, which is a weak version of the $k$-linear cone restriction
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On a multiplicity formula for spherical varieties J. Eur. Math. Soc. (IF 2.6) Pub Date : 2021-11-17 Chen Wan
In this paper, we propose a conjectural multiplicity formula for general spherical varieties. For all the cases where a multiplicity formula has been proved, including Whittaker models, Gan–Gross–Prasad models, Ginzburg–Rallis models, Galois models and Shalika models, we show that the multiplicity formulas in our conjecture are the same as the multiplicity formulas that have been proved. We also prove
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The sensitivity conjecture, induced subgraphs of cubes, and Clifford algebras J. Eur. Math. Soc. (IF 2.6) Pub Date : 2021-11-15 Daniel V. Mathews
We give another version of Huang's proof that an induced subgraph of the n-dimensional cube graph containing over half the vertices has maximal degree at least $\sqrt{n}$, which implies the Sensitivity Conjecture. This argument uses Clifford algebras of positive definite signature in a natural way. We also prove a weighted version of the result.
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Cichoń’s maximum without large cardinals J. Eur. Math. Soc. (IF 2.6) Pub Date : 2021-11-09 Martin Goldstern,Jakob Kellner,Diego A. Mejía,Saharon Shelah
Cichon's diagram lists twelve cardinal characteristics (and the provable inequalities between them) associated with the ideals of null sets, meager sets, countable sets, and $\sigma$-compact subsets of the irrationals. It is consistent that all entries of Cichon's diagram are pairwise different (apart from $\textrm{add}(\mathcal{M})$ and $\textrm{cof}(\mathcal{M})$, which are provably equal to other
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Global existence of entropy-weak solutions to the compressible Navier–Stokes equations with non-linear density dependent viscosities J. Eur. Math. Soc. (IF 2.6) Pub Date : 2021-11-09 Didier Bresch,Alexis Vasseur,Cheng Yu
In this paper, we extend considerably the global existence results of entropy-weak solutions related to compressible Navier-Stokes system with density dependent viscosities obtained, independently (using different strategies), by Vasseur-Yu [Inventiones mathematicae (2016) and arXiv:1501.06803 (2015)] and by Li-Xin [arXiv:1504.06826 (2015)].More precisely we are able to consider a physical symmetric
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$\mathbb{C}$-motivic modular forms J. Eur. Math. Soc. (IF 2.6) Pub Date : 2021-11-09 Bogdan Gheorghe, Daniel C. Isaksen, Achim Krause, Nicolas Ricka
We construct a topological model for cellular, 2-complete, stable $\mathbb{C}$-motivic homotopy theory that uses no algebro-geometric foundations. We compute the Steenrod algebra in this context, and we construct a “motivic modular forms” spectrum over $\mathbb{C}$.
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$C^r$-prevalence of stable ergodicity for a class of partially hyperbolic systems J. Eur. Math. Soc. (IF 2.6) Pub Date : 2021-11-09 Martin Leguil, Zhiyuan Zhang
We prove that for $r \in \mathbb{N}_{\geq 2} \cup \{\infty\}$, for any dynamically coherent, center bunched and strongly pinched volume preserving $C^r$ partially hyperbolic diffeomorphism $f \colon X \to X$, if either (1) its center foliation is uniformly compact, or (2) its center-stable and center-unstable foliations are of class $C^1$, then there exists a $C^1$-open neighborhood of $f$ in $\op
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Irreducible modules for pseudo-reductive groups J. Eur. Math. Soc. (IF 2.6) Pub Date : 2021-11-09 Michael Bate, David I. Stewart
We classify the irreducible representations of smooth, connected affine algebraic groups over a field, by tackling the case of pseudo-reductive groups. We reduce the problem of calculating the dimension for pseudo-split pseudo-reductive groups to the split reductive case and the pseudo-split pseudo-reductive commutative case. Moreover, we give the first results on the latter, including a rather complete