
样式: 排序: IF: - GO 导出 标记为已读
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Suppression of Chemotactic Singularity by Buoyancy Geom. Funct. Anal. (IF 2.4) Pub Date : 2025-02-13 Zhongtian Hu, Alexander Kiselev, Yao Yao
Chemotactic singularity formation in the context of the Patlak-Keller-Segel equation is an extensively studied phenomenon. In recent years, it has been shown that the presence of fluid advection can arrest the singularity formation given that the fluid flow possesses mixing or diffusion enhancing properties and its amplitude is sufficiently strong - this effect is conjectured to hold for more general
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Uniqueness of Tangent Flows at Infinity for Finite-Entropy Shortening Curves Geom. Funct. Anal. (IF 2.4) Pub Date : 2025-02-13 Kyeongsu Choi, Dong-Hwi Seo, Wei-Bo Su, Kai-Wei Zhao
In this paper, we prove that an ancient smooth curve-shortening flow with finite entropy embedded in \(\mathbb{R}^{2}\) has a unique tangent flow at infinity. To this end, we show that its rescaled flows backwardly converge to a line with multiplicity m≥3 exponentially fast in any compact region, unless the flow is a shrinking circle, a static line, a paper clip, or a translating grim reaper. In addition
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On the Spielman-Teng Conjecture Geom. Funct. Anal. (IF 2.4) Pub Date : 2025-02-13 Ashwin Sah, Julian Sahasrabudhe, Mehtaab Sawhney
Let M be an n×n matrix with iid subgaussian entries with mean 0 and variance 1 and let σn(M) denote the least singular value of M. We prove that $$ \mathbb{P}\big( \sigma _{n}(M) \leqslant \varepsilon n^{-1/2} \big) = (1+o(1)) \varepsilon + e^{- \Omega (n)} $$ for all 0⩽ε≪1. This resolves, up to a 1+o(1) factor, a seminal conjecture of Spielman and Teng.
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Geometric Langlands Duality for Periods Geom. Funct. Anal. (IF 2.4) Pub Date : 2025-02-06 Tony Feng, Jonathan Wang
We study conjectures of Ben-Zvi–Sakellaridis–Venkatesh that categorify the relationship between automorphic periods and L-functions in the context of the Geometric Langlands equivalence. We provide evidence for these conjectures in some low-rank examples, by using derived Fourier analysis and the theory of chiral algebras to categorify the Rankin-Selberg unfolding method.
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Optimal Rigidity and Maximum of the Characteristic Polynomial of Wigner Matrices Geom. Funct. Anal. (IF 2.4) Pub Date : 2025-02-05 Paul Bourgade, Patrick Lopatto, Ofer Zeitouni
We determine to leading order the maximum of the characteristic polynomial for Wigner matrices and β-ensembles. In the special case of Gaussian-divisible Wigner matrices, our method provides universality of the maximum up to tightness. These are the first universal results on the Fyodorov–Hiary–Keating conjectures for these models, and in particular answer the question of optimal rigidity for the spectrum
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Invariant Subvarieties of Minimal Homological Dimension, Zero Lyapunov Exponents, and Monodromy Geom. Funct. Anal. (IF 2.4) Pub Date : 2025-02-03 Paul Apisa
We classify the \(\mathrm{GL}(2,\mathbb{R})\)-invariant subvarieties \(\mathcal{M}\) in strata of Abelian differentials for which any two \(\mathcal{M}\)-parallel cylinders have homologous core curves. As a corollary we show that outside of an explicit list of exceptions, if \(\mathcal{M}\) is a \(\mathrm{GL}(2,\mathbb{R})\)-invariant subvariety, then the Kontsevich-Zorich cocycle has nonzero Lyapunov
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Unit and Distinct Distances in Typical Norms Geom. Funct. Anal. (IF 2.4) Pub Date : 2025-01-24 Noga Alon, Matija Bucić, Lisa Sauermann
Erdős’ unit distance problem and Erdős’ distinct distances problem are among the most classical and well-known open problems in discrete mathematics. They ask for the maximum number of unit distances, or the minimum number of distinct distances, respectively, determined by n points in the Euclidean plane. The question of what happens in these problems if one considers normed spaces other than the Euclidean
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Optimal Transport Between Algebraic Hypersurfaces Geom. Funct. Anal. (IF 2.4) Pub Date : 2025-01-22 Paolo Antonini, Fabio Cavalletti, Antonio Lerario
What is the optimal way to deform a projective hypersurface into another one? In this paper we will answer this question adopting the point of view of measure theory, introducing the optimal transport problem between complex algebraic projective hypersurfaces. First, a natural topological embedding of the space of hypersurfaces of a given degree into the space of measures on the projective space is
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Lagrangian Subvarieties of Hyperspherical Varieties Geom. Funct. Anal. (IF 2.4) Pub Date : 2025-01-22 Michael Finkelberg, Victor Ginzburg, Roman Travkin
Given a hyperspherical G-variety 𝒳 we consider the zero moment level Λ𝒳⊂𝒳 of the action of a Borel subgroup B⊂G. We conjecture that Λ𝒳 is Lagrangian. For the dual G∨-variety 𝒳∨, we conjecture that that there is a bijection between the sets of irreducible components \(\operatorname {Irr}\Lambda _{{\mathscr{X}}}\) and \(\operatorname {Irr}\Lambda _{{\mathscr{X}}^{\vee }}\). We check this conjecture
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On the Distance Sets Spanned by Sets of Dimension d/2 in $\mathbb{R}^{d}$ Geom. Funct. Anal. (IF 2.4) Pub Date : 2025-01-09 Pablo Shmerkin, Hong Wang
We establish the dimension version of Falconer’s distance set conjecture for sets of equal Hausdorff and packing dimension (in particular, for Ahlfors-regular sets) in all ambient dimensions. In dimensions d=2 or 3, we obtain the first explicit improvements over the classical 1/2 bound for the dimensions of distance sets of general Borel sets of dimension d/2. For example, we show that the set of distances
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The Hadwiger Theorem on Convex Functions, I Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-10-16 Andrea Colesanti, Monika Ludwig, Fabian Mussnig
A complete classification of all continuous, epi-translation and rotation invariant valuations on the space of super-coercive convex functions on \({\mathbb{R}}^{n}\) is established. The valuations obtained are functional versions of the classical intrinsic volumes. For their definition, singular Hessian valuations are introduced.
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Geometric Regularity of Blow-up Limits of the Kähler-Ricci Flow Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-10-16 Max Hallgren, Wangjian Jian, Jian Song, Gang Tian
We establish geometric regularity for Type I blow-up limits of the Kähler-Ricci flow based at any sequence of Ricci vertices. As a consequence, the limiting flow is continuous in time in both Gromov-Hausdorff and Gromov-W1 distances. In particular, the singular sets of each time slice and its tangent cones are closed and of codimension no less than 4.
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Universality and Sharp Matrix Concentration Inequalities Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-10-10 Tatiana Brailovskaya, Ramon van Handel
We show that, under mild assumptions, the spectrum of a sum of independent random matrices is close to that of the Gaussian random matrix whose entries have the same mean and covariance. This nonasymptotic universality principle yields sharp matrix concentration inequalities for general sums of independent random matrices when combined with the Gaussian theory of Bandeira, Boedihardjo, and Van Handel
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Birkhoff Conjecture for Nearly Centrally Symmetric Domains Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-10-10 V. Kaloshin, C. E. Koudjinan, Ke Zhang
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Gromov-Witten Invariants in Complex and Morava-Local K-Theories Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-10-07 Mohammed Abouzaid, Mark McLean, Ivan Smith
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Direct Products of Free Groups in Aut(FN) Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-08-05 Martin R. Bridson, Richard D. Wade
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Maximal Multiplicity of Laplacian Eigenvalues in Negatively Curved Surfaces Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-07-25 Cyril Letrouit, Simon Machado
In this work, we obtain the first upper bound on the multiplicity of Laplacian eigenvalues for negatively curved surfaces which is sublinear in the genus g. Our proof relies on a trace argument for the heat kernel, and on the idea of leveraging an r-net in the surface to control this trace. This last idea was introduced in 2021 for similar spectral purposes in the context of graphs of bounded degree
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Virtually Free-by-Cyclic Groups Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-07-22 Dawid Kielak, Marco Linton
We obtain a homological characterisation of virtually free-by-cyclic groups among groups that are hyperbolic and virtually compact special. As a consequence, we show that many groups known to be coherent actually possess the stronger property of being virtually free-by-cyclic. In particular, we show that all one-relator groups with torsion are virtually free-by-cyclic, solving a conjecture of Baumslag
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Mass Equidistribution for Saito-Kurokawa Lifts Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-07-23 Jesse Jääsaari, Stephen Lester, Abhishek Saha
Let F be a holomorphic cuspidal Hecke eigenform for \(\mathrm{Sp}_{4}({\mathbb{Z}})\) of weight k that is a Saito–Kurokawa lift. Assuming the Generalized Riemann Hypothesis (GRH), we prove that the mass of F equidistributes on the Siegel modular variety as k⟶∞. As a corollary, we show under GRH that the zero divisors of Saito–Kurokawa lifts equidistribute as their weights tend to infinity.
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Disk-Like Surfaces of Section and Symplectic Capacities Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-07-16 O. Edtmair
We prove that the cylindrical capacity of a dynamically convex domain in \({\mathbb{R}}^{4}\) agrees with the least symplectic area of a disk-like global surface of section of the Reeb flow on the boundary of the domain. Moreover, we prove the strong Viterbo conjecture for all convex domains in \({\mathbb{R}}^{4}\) which are sufficiently C3 close to the round ball. This generalizes a result of Abb
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The Singular Support of Sheaves Is γ-Coisotropic Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-07-01 Stéphane Guillermou, Claude Viterbo
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Fusion and Positivity in Chiral Conformal Field Theory Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-06-27 James E. Tener
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Growth of k-Dimensional Systoles in Congruence Coverings Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-06-05 Mikhail Belolipetsky, Shmuel Weinberger
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Rigidity Theorems for Higher Rank Lattice Actions Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-05-29 Homin Lee
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The Parabolic U(1)-Higgs Equations and Codimension-Two Mean Curvature Flows Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-05-29 Davide Parise, Alessandro Pigati, Daniel Stern
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Equilibrium States of Endomorphisms of $\mathbb{P}^{k}$ : Spectral Stability and Limit Theorems Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-05-13 Fabrizio Bianchi, Tien-Cuong Dinh
We establish the existence of a spectral gap for the transfer operator induced on \(\mathbb{P}^{k} = \mathbb{P}^{k} (\mathbb{C})\) by a generic holomorphic endomorphism and a suitable continuous weight and its perturbations on various functional spaces, which is new even in dimension one. Thanks to the spectral gap, we establish an exponential speed of convergence for the equidistribution of the backward
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Lagrangians, SO(3)-Instantons and Mixed Equation Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-05-02 Aliakbar Daemi, Kenji Fukaya, Maksim Lipyanskiy
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Commensurations of Aut(FN) and Its Torelli Subgroup Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-04-22 Martin R. Bridson, Richard D. Wade
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Sections and Unirulings of Families over $\mathbb{P}^{1}$ Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-04-18 Alex Pieloch
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Dominated Splitting from Constant Periodic Data and Global Rigidity of Anosov Automorphisms Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-04-15 Jonathan DeWitt, Andrey Gogolev
We show that a \(\operatorname{GL}(d,\mathbb{R})\) cocycle over a hyperbolic system with constant periodic data has a dominated splitting whenever the periodic data indicates it should. This implies global periodic data rigidity of generic Anosov automorphisms of \(\mathbb{T}^{d}\). Further, our approach also works when the periodic data is narrow, that is, sufficiently close to constant. We can show
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Large Genus Bounds for the Distribution of Triangulated Surfaces in Moduli Space Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-03-04 Sahana Vasudevan
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Coalescence of Geodesics and the BKS Midpoint Problem in Planar First-Passage Percolation Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-02-21 Barbara Dembin, Dor Elboim, Ron Peled
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Augmentations, Fillings, and Clusters Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-02-21 Honghao Gao, Linhui Shen, Daping Weng
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On Closed Geodesics in Lorentz Manifolds Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-02-15 S. Allout, A. Belkacem, A. Zeghib
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A New Complete Two-Dimensional Shrinking Gradient Kähler-Ricci Soliton Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-02-14 Richard H. Bamler, Charles Cifarelli, Ronan J. Conlon, Alix Deruelle
We prove the existence of a unique complete shrinking gradient Kähler-Ricci soliton with bounded scalar curvature on the blowup of \(\mathbb{C}\times \mathbb{P}^{1}\) at one point. This completes the classification of such solitons in two complex dimensions.
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Non-isomorphism of A∗n,2≤n≤∞, for a non-separable abelian von Neumann algebra A Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-02-14 Rémi Boutonnet, Daniel Drimbe, Adrian Ioana, Sorin Popa
We prove that if A is a non-separable abelian tracial von Neuman algebra then its free powers A∗n,2≤n≤∞, are mutually non-isomorphic and with trivial fundamental group, \(\mathcal{F}(A^{*n})=1\), whenever 2≤n<∞. This settles the non-separable version of the free group factor problem.
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Weakly Bounded Cohomology Classes and a Counterexample to a Conjecture of Gromov Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-02-14 Dario Ascari, Francesco Milizia
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Homology Growth, Hyperbolization, and Fibering Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-02-14 Grigori Avramidi, Boris Okun, Kevin Schreve
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Quasiregular Values and Rickman’s Picard Theorem Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-02-14 Ilmari Kangasniemi, Jani Onninen
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Partial Hyperbolicity and Pseudo-Anosov Dynamics Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-02-07 Sergio R. Fenley, Rafael Potrie
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A Metric Fixed Point Theorem and Some of Its Applications Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-02-07 Anders Karlsson
A general fixed point theorem for isometries in terms of metric functionals is proved under the assumption of the existence of a conical bicombing. It is new for isometries of convex sets of Banach spaces as well as for non-locally compact CAT(0)-spaces and injective spaces. Examples of actions on non-proper CAT(0)-spaces come from the study of diffeomorphism groups, birational transformations, and
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On the Almost Reducibility Conjecture Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-02-05 Lingrui Ge
Avila’s Almost Reducibility Conjecture (ARC) is a powerful statement linking purely analytic and dynamical properties of analytic one-frequency \(SL(2,{\mathbb{R}})\) cocycles. It is also a fundamental tool in the study of spectral theory of analytic one-frequency Schrödinger operators, with many striking consequences, allowing to give a detailed characterization of the subcritical region. Here we
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On the Dimension of Exceptional Parameters for Nonlinear Projections, and the Discretized Elekes-Rónyai Theorem Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-02-05 Orit E. Raz, Joshua Zahl
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Kaufman and Falconer Estimates for Radial Projections and a Continuum Version of Beck’s Theorem Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-02-05 Tuomas Orponen, Pablo Shmerkin, Hong Wang
We provide several new answers on the question: how do radial projections distort the dimension of planar sets? Let \(X,Y \subset \mathbb{R}^{2}\) be non-empty Borel sets. If X is not contained in any line, we prove that $$ \sup _{x \in X} \dim _{\mathrm {H}}\pi _{x}(Y \, \setminus \, \{x\}) \geq \min \{ \dim _{\mathrm {H}}X,\dim _{\mathrm {H}}Y,1\}. $$ If dimHY>1, we have the following improved lower
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CAT(0) Spaces of Higher Rank I Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-02-02 Stephan Stadler
A CAT(0) space has rank at least n if every geodesic lies in an n-flat. Ballmann’s Higher Rank Rigidity Conjecture predicts that a CAT(0) space of rank at least 2 with a geometric group action is rigid – isometric to a Riemannian symmetric space, a Euclidean building, or splits as a metric product. This paper is the first in a series motivated by Ballmann’s conjecture. Here we prove that a CAT(0) space
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Mean Convex Smoothing of Mean Convex Cones Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-02-01 Zhihan Wang
We show that any minimizing hypercone can be perturbed into one side to a properly embedded smooth minimizing hypersurface in the Euclidean space, and every viscosity mean convex cone admits a properly embedded smooth mean convex self-expander asymptotic to it near infinity. These two together confirm a conjecture of Lawson (Geom. Meas. Theor. Calcu. Var. 44:441, 1986, Problem 5.7).
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Two Rigidity Results for Stable Minimal Hypersurfaces Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-02-01 Giovanni Catino, Paolo Mastrolia, Alberto Roncoroni
The aim of this paper is to prove two results concerning the rigidity of complete, immersed, orientable, stable minimal hypersurfaces: we show that they are hyperplane in R4, while they do not exist in positively curved closed Riemannian (n+1)-manifold when n≤5; in particular, there are no stable minimal hypersurfaces in Sn+1 when n≤5. The first result was recently proved also by Chodosh and Li, and
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Extremal Affine Subspaces and Khintchine-Jarník Type Theorems Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-02-01 Jing-Jing Huang
We prove a conjecture of Kleinbock which gives a clear-cut classification of all extremal affine subspaces of \(\mathbb{R}^{n}\). We also give an essentially complete classification of all Khintchine type affine subspaces, except for some boundary cases within two logarithmic scales. More general Jarník type theorems are proved as well, sometimes without the monotonicity of the approximation function
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Odd Distances in Colourings of the Plane Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-01-30 James Davies
We prove that every finite colouring of the plane contains a monochromatic pair of points at an odd distance from each other.
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A New Regularized Siegel-Weil Type Formula. Part I Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-01-22 David Ginzburg, David Soudry
In this paper, we prove a formula, realizing certain residual Eisenstein series on symplectic groups as regularized kernel integrals. These Eisenstein series, as well as the kernel integrals, are attached to Speh representations. This forms an initial step to a new type of a regularized Siegel-Weil formula that we propose. This new formula bears the same relation to the generalized doubling integrals
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Relations between scaling exponents in unimodular random graphs Geom. Funct. Anal. (IF 2.4) Pub Date : 2023-11-09 James R. Lee
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GOE statistics on the moduli space of surfaces of large genus Geom. Funct. Anal. (IF 2.4) Pub Date : 2023-11-02 Zeév Rudnick
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Bers’ simultaneous uniformization and the intersection of Poincaré holonomy varieties Geom. Funct. Anal. (IF 2.4) Pub Date : 2023-10-31 Shinpei Baba
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Classical wave methods and modern gauge transforms: spectral asymptotics in the one dimensional case Geom. Funct. Anal. (IF 2.4) Pub Date : 2023-10-31 Jeffrey Galkowski, Leonid Parnovski, Roman Shterenberg
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Concentration of invariant means and dynamics of chain stabilizers in continuous geometries Geom. Funct. Anal. (IF 2.4) Pub Date : 2023-10-12 Friedrich Martin Schneider
We prove a concentration inequality for invariant means on topological groups, namely for such adapted to a chain of amenable topological subgroups. The result is based on an application of Azuma’s martingale inequality and provides a method for establishing extreme amenability. Building on this technique, we exhibit new examples of extremely amenable groups arising from von Neumann’s continuous geometries
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Contribution of n-cylinder square-tiled surfaces to Masur–Veech volume of $\mathcal{H}(2g-2)$ Geom. Funct. Anal. (IF 2.4) Pub Date : 2023-10-12 Ivan Yakovlev
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A nonabelian Brunn–Minkowski inequality Geom. Funct. Anal. (IF 2.4) Pub Date : 2023-07-05 Yifan Jing, Chieu-Minh Tran, Ruixiang Zhang
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Tori Approximation of Families of Diagonally Invariant Measures Geom. Funct. Anal. (IF 2.4) Pub Date : 2023-07-04 Omri Nisan Solan, Yuval Yifrach
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Approximate Lattices in Higher-Rank Semi-Simple Groups Geom. Funct. Anal. (IF 2.4) Pub Date : 2023-06-30 Simon Machado
We show that strong approximate lattices in higher-rank semi-simple algebraic groups are arithmetic.