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Extremal Numbers and Sidorenko’s Conjecture Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-04-24 David Conlon, Joonkyung Lee, Alexander Sidorenko
Sidorenko’s conjecture states that, for all bipartite graphs $H$, quasirandom graphs contain asymptotically the minimum number of copies of $H$ taken over all graphs with the same order and edge density. While still open for graphs, the analogous statement is known to be false for hypergraphs. We show that there is some advantage in this, in that if Sidorenko’s conjecture does not hold for a particular
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Multimatroids and Rational Curves with Cyclic Action Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-04-23 Emily Clader, Chiara Damiolini, Christopher Eur, Daoji Huang, Shiyue Li
We study the connection between multimatroids and moduli spaces of rational curves with cyclic action. Multimatroids are generalizations of matroids and delta-matroids that naturally arise in topological graph theory. The perspective of moduli of curves provides a tropical framework for studying multimatroids, generalizing the previous connection between type-$A$ permutohedral varieties (Losev–Manin
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Log-Concavity of the Alexander Polynomial Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-04-23 Elena S Hafner, Karola Mészáros, Alexander Vidinas
The central question of knot theory is that of distinguishing links up to isotopy. The first polynomial invariant of links devised to help answer this question was the Alexander polynomial (1928). Almost a century after its introduction, it still presents us with tantalizing questions, such as Fox’s conjecture (1962) that the absolute values of the coefficients of the Alexander polynomial $\Delta _{L}(t)$
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Basic Remarks on Lagrangian Submanifolds of Hyperkähler Manifolds Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-04-23 René Mboro
This note presents basic restrictions on the topology of Lagrangian surfaces of hyper-Kähler $4$-folds and a remark on the interaction of a Lagrangian subvariety of a hyper-Kähler variety with a Lagrangian fibration of the latter.
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Surfaces of General Type with Maximal Picard Number Near the Noether Line Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-04-22 Nguyen Bin, Vicente Lorenzo
The first published non-trivial examples of algebraic surfaces of general type with maximal Picard number are due to Persson, who constructed surfaces with maximal Picard number on the Noether line $K^{2}=2\chi -6$ for every admissible pair $(K^{2},\chi )$ such that $\chi \not \equiv 0 \ \text {mod}\ 6$. In this note, given a non-negative integer $k$, algebraic surfaces of general type with maximal
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A Facial Order for Torsion Classes Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-04-22 Eric J Hanson
We generalize the “facial weak order” of a finite Coxeter group to a partial order on a set of intervals in a complete lattice. We apply our construction to the lattice of torsion classes of a finite-dimensional algebra and consider its restriction to intervals coming from stability conditions. We give two additional interpretations of the resulting “facial semistable order”: one using cover relations
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A Construction of Deformations to General Algebras Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-04-22 David Bowman, Dora Puljić, Agata Smoktunowicz
One of the questions investigated in deformation theory is to determine to which algebras can a given associative algebra be deformed. In this paper we investigate a different but related question, namely: for a given associative finite-dimensional ${\mathbb{C}}$-algebra $A$, find algebras $N$, which can be deformed to $A$. We develop a simple method that produces associative and flat deformations
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On the ∂—-Equation with L2 Estimates on Singular Complex Spaces Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-04-22 Zhenqian Li, Zhi Li, Xiangyu Zhou
In this paper, we present the unsolvability of $\overline \partial $-equation with weighted $L^{2}$ estimates involved curvature terms on any singular normal complex space in general. Moreover, in the non-normal case, we also give a complete description on $L^{2}$-solvability of the $\overline \partial $-equation with weighted $L^{2}$ estimates for plane curve singularities and their variants in the
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On Chow Rings of Quiver Moduli Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-04-19 Pieter Belmans, Hans Franzen
We describe the point class and Todd class in the Chow ring of a moduli space of quiver representations, building on a result of Ellingsrud–Strømme. This, together with the presentation of the Chow ring by the second author, makes it possible to compute integrals on quiver moduli. To do so, we construct a canonical morphism of universal representations in great generality, and along the way point out
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Transitive Centralizer and Fibered Partially Hyperbolic Systems Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-04-18 Danijela Damjanović, Amie Wilkinson, Disheng Xu
We prove several rigidity results about the centralizer of a smooth diffeomorphism, concentrating on two families of examples: diffeomorphisms with transitive centralizer, and perturbations of isometric extensions of Anosov diffeomorphisms of nilmanifolds. We classify all smooth diffeomorphisms with transitive centralizer: they are exactly the maps that preserve a principal fiber bundle structure,
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Duality in the Directed Landscape and Its Applications to Fractal Geometry Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-04-08 Manan Bhatia
Geodesic coalescence, or the tendency of geodesics to merge together, is a hallmark phenomenon observed in a variety of planar random geometries involving a random distortion of the Euclidean metric. As a result of this, the union of interiors of all geodesics going to a fixed point tends to form a tree-like structure that is supported on a vanishing fraction of the space. Such geodesic trees exhibit
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The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-04-08 Andrew Campbell, Sean O’Rourke, David Renfrew
We extend the free convolution of Brown measures of $R$-diagonal elements introduced by Kösters and Tikhomirov [ 28] to fractional powers. We then show how this fractional free convolution arises naturally when studying the roots of random polynomials with independent coefficients under repeated differentiation. When the proportion of derivatives to the degree approaches one, we establish central limit
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Joint Moments of Higher Order Derivatives of CUE Characteristic Polynomials I: Asymptotic Formulae Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-04-06 Jonathan P Keating, Fei Wei
We derive explicit asymptotic formulae for the joint moments of the $n_{1}$-th and $n_{2}$-th derivatives of the characteristic polynomials of Circular Unitary Ensemble random matrices for any non-negative integers $n_{1}, n_{2}$. These formulae are expressed in terms of determinants whose entries involve modified Bessel functions of the first kind. We also express them in terms of two types of combinatorial
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Correction to the paper “The polynomial sieve and equal sums of like polynomials” (IMRN, Vol. 2015, No. 7, 1987–2019) Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-04-05 Tim D Browning
This paper corrects an error in an earlier work of the author.
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Slope Boundedness and Equidistribution Theorem Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-04-05 Wenbin Luo
In this article, we prove the boundedness of minimal slopes of adelic line bundles over function fields of characteristic $0$. This can be applied to prove the equidistribution of generic and small points with respect to a big and semipositive adelic line bundle. Our methods can be applied to the finite places of number fields as well. We also show the continuity of $\chi $-volumes over function fields
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The Moduli Space of Cyclic Covers in Positive Characteristic Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-04-05 Huy Dang, Matthias Hippold
We study the $p$-rank stratification of the moduli space $\operatorname{\mathcal{A}\mathcal{S}\mathcal{W}}_{(d_{1},d_{2},\ldots ,d_{n})}$, which represents $\mathbb{Z}/p^{n}$-covers in characteristic $p>0$ whose $\mathbb{Z}/p^{i}$-subcovers have conductor $d_{i}$. In particular, we identify the irreducible components of the moduli space and determine their dimensions. To achieve this, we analyze the
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Derived Equivalence for Elliptic K3 Surfaces and Jacobians Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-04-04 Reinder Meinsma, Evgeny Shinder
We present a detailed study of elliptic fibrations on Fourier-Mukai partners of K3 surfaces, which we call derived elliptic structures. We fully classify derived elliptic structures in terms of Hodge-theoretic data, similar to the Derived Torelli Theorem that describes Fourier-Mukai partners. In Picard rank two, derived elliptic structures are fully determined by the Lagrangian subgroups of the discriminant
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Limiting Distribution of Dense Orbits in a Moduli Space of Rank m Discrete Subgroups in (m+1)-Space Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-04-03 Michael Bersudsky, Hao Xing
We study the limiting distribution of dense orbits of a lattice subgroup $\Gamma \leq \textrm{SL}(m+1,\mathbb{R})$ acting on $H\backslash \textrm{SL}(m+1,\mathbb{R})$, with respect to a filtration of growing norm balls. The novelty of our work is that the groups $H$ we consider have infinitely many non-trivial connected components. For a specific such $H$, the homogeneous space $H\backslash G$ identifies
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Bounding Radon Numbers via Betti Numbers Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-04-03 Zuzana Patáková
We prove general topological Radon-type theorems for sets in $\mathbb R^{d}$ or on a surface. Combined with a recent result of Holmsen and Lee, we also obtain fractional Helly theorem, and consequently the existence of weak $\varepsilon $-nets as well as a $(p,q)$-theorem for those sets. More precisely, given a family ${\mathcal{F}}$ of subsets of ${\mathbb{R}}^{d}$, we will measure the homological
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Minimal Diffeomorphisms with L1 Hopf Differentials Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-04-02 Nathaniel Sagman
We prove that for any two Riemannian metrics $\sigma _{1}, \sigma _{2}$ on the unit disk, a homeomorphism $\partial \mathbb{D}\to \partial \mathbb{D}$ extends to at most one quasiconformal minimal diffeomorphism $(\mathbb{D},\sigma _{1})\to (\mathbb{D},\sigma _{2})$ with $L^{1}$ Hopf differential. For minimal Lagrangian diffeomorphisms between hyperbolic disks, the result is known, but this is the
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A Formalism of F-modules for Rings with Complete Local Finite F-Representation Type Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-04-02 Eamon Quinlan-Gallego
We develop a formalism of unit $F$-modules in the style of Lyubeznik and Emerton-Kisin for rings that have finite $F$-representation type after localization and completion at every prime ideal. As applications, we show that if $R$ is such a ring then the iterated local cohomology modules $H^{n_{1}}_{I_{1}} \circ \cdots \circ H^{n_{s}}_{I_{s}}(R)$ have finitely many associated primes, and that all local
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Decorated Discrete Conformal Maps and Convex Polyhedral Cusps Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-04-02 Alexander I Bobenko, Carl O R Lutz
We discuss a notion of discrete conformal equivalence for decorated piecewise Euclidean surfaces (PE-surface), that is, PE-surfaces with a choice of circle about each vertex. It is closely related to inversive distance and hyperideal circle patterns. Under the assumption that the circles are non-intersecting, we prove the corresponding discrete uniformization theorem. The uniformization theorem for
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Arithmetic Trialitarian Hyperbolic Lattices Are Not Locally Extended Residually Finite Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-04-02 Nikolay Bogachev, Leone Slavich, Hongbin Sun
A group is LERF (locally extended residually finite) if all its finitely generated subgroups are separable. We prove that the trialitarian arithmetic lattices in $\mathbf{PSO}_{7,1}(\mathbb{R})$ are not LERF. This result, together with previous work by the third author, implies that no arithmetic lattice in $\mathbf{PO}_{n,1}(\mathbb{R})$, $n>3$, is LERF.
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Pentagram Rigidity for Centrally Symmetric Octagons Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-04-02 Richard Evan Schwartz
In this paper I will establish a special case of a conjecture that intertwines the deep diagonal pentagram maps and Poncelet polygons. The special case is that of the $3$-diagonal map acting on affine equivalence classes of centrally symmetric octagons. The proof involves establishing that the map is Arnold-Liouville integrable in this case, and then exploring the Lagrangian surface foliation in detail
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Neutralized Local Entropy and Dimension bounds for Invariant Measures Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-03-26 S Ben Ovadia, F Rodriguez-Hertz
We introduce a notion of a point-wise entropy of measures (i.e., local entropy) called neutralized local entropy, and compare it with the Brin-Katok local entropy. We show that the neutralized local entropy coincides with Brin-Katok local entropy almost everywhere. Neutralized local entropy is computed by measuring open sets with a relatively simple geometric description. Our proof uses a measure density
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Approximation by BV-extension Sets via Perimeter Minimization in Metric Spaces Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-03-22 Jesse Koivu, Danka Lučić, Tapio Rajala
We show that every bounded domain in a metric measure space can be approximated in measure from inside by closed $BV$-extension sets. The extension sets are obtained by minimizing the sum of the perimeter and the measure of the difference between the domain and the set. By earlier results, in PI spaces the minimizers have open representatives with locally quasiminimal surface. We give an example in
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Periodicity of Hitchin’s Uniformizing Higgs Bundles Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-03-22 Raju Krishnamoorthy, Mao Sheng
Let $C$ be a smooth projective curve over ${{\mathbb{C}}}$. We link the periodicity of Hitchin’s uniformizing Higgs bundle of $C$ with the underlying arithmetic geometry of the curve. Some new relations are discovered. We also speculate on the whole class of periodic Higgs bundles.
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The Koszul Complex and a Certain Induced Module for a Quantum group Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-03-22 Toshiyuki Tanisaki
We give a description of a certain induced module for a quantum group of type $A$. Together with our previous results this gives a proof of Lusztig’s conjectural multiplicity formula for non-restricted modules over the De Concini-Kac type quantized enveloping algebra of type $A_{n}$ at the $\ell $-th root of unity, where $\ell $ is an odd integer satisfying $(\ell ,n+1)=1$ and $\ell> n+1$.
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Determinantal Representations and the Image of the Principal Minor Map Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-03-20 Abeer Al Ahmadieh, Cynthia Vinzant
In this paper we explore determinantal representations of multiaffine polynomials and consequences for the image of various spaces of matrices under the principal minor map. We show that a real multiaffine polynomial has a definite Hermitian determinantal representation if and only if all of its so-called Rayleigh differences factor as Hermitian squares and use this characterization to conclude that
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Maximality Properties of Generalized Springer Representations of SO (N, ℂ) Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-03-20 Ruben La
Let $C$ be a unipotent class of $G=\textrm{SO}(N,\mathbb{C})$, $\mathcal{E}$ an irreducible $G$-equivariant local system on $C$. The generalized Springer representation $\rho (C,\mathcal{E})$ appears in the top cohomology of some variety. Let $\bar \rho (C,\mathcal{E})$ be the representation obtained by summing over all cohomology groups of this variety. It is well known that $\rho (C,\mathcal{E})$
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Birational Transformations on Irreducible Compact Hermitian Symmetric Spaces Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-03-15 Cong Ding
We construct a sequence of explicit blow-ups and blow-downs on an irreducible compact Hermitian symmetric spaces $X$ which transforms it into a projective space of the same dimension. Moreover, this resolves a birational map given by Landsberg and Manivel. Centers of the blow-ups for $X$ are constructed by loci of chains of minimal rational curves and centers of the blow-ups for the projective space
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Linkage and F-Regularity of Determinantal Rings Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-03-15 Vaibhav Pandey, Yevgeniya Tarasova
In this paper, we prove that the generic link of a generic determinantal ring defined by maximal minors is strongly $F$-regular. In the process, we strengthen a result of Chardin and Ulrich in the graded setting. They showed that the generic residual intersections of a complete intersection ring with rational singularities again have rational singularities. We show that if the said complete intersection
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Drinfeld’s Lemma for F-isocrystals, I Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-03-15 Kiran S Kedlaya
We prove that in either the convergent or overconvergent setting, an absolutely irreducible $F$-isocrystal on the absolute product of two or more smooth schemes over perfect fields of characteristic $p$, further equipped with actions of the partial Frobenius maps, is an external product of $F$-isocrystals over the multiplicands. The corresponding statement for lisse $\overline{{\mathbb{Q}}}_{\ell }$-sheaves
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Bounds for Rational Points on Algebraic Curves, Optimal in the Degree, and Dimension Growth Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-03-05 Gal Binyamini, Raf Cluckers, Dmitry Novikov
Bounding the number of rational points of height at most $H$ on irreducible algebraic plane curves of degree $d$ has been an intense topic of investigation since the work by Bombieri and Pila. In this paper we establish optimal dependence on $d$ by showing the upper bound $C d^{2} H^{2/d} (\log H)^{\kappa }$ with some absolute constants $C$ and $\kappa $. This bound is optimal with respect to both
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Differential Graded Manifolds of Finite Positive Amplitude Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-02-29 Kai Behrend, Hsuan-Yi Liao, Ping Xu
We prove that dg manifolds of finite positive amplitude, that is, bundles of positively graded curved $L_{\infty }[1]$-algebras, form a category of fibrant objects. As a main step in the proof, we obtain a factorization theorem using path spaces. First we construct an infinite-dimensional factorization of a diagonal morphism using actual path spaces motivated by the AKSZ construction. Then we cut down
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Rectifiability of Flat Singular Points for Area-Minimizing mod 2Q Hypercurrents Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-02-29 Anna Skorobogatova
Consider an $ m $-dimensional area minimizing mod$ (2Q) $ current $ T $, with $ Q\in {\mathbb {N}} $, inside a sufficiently regular Riemannian manifold of dimension $ m + 1 $. We show that the set of singular density-$ Q $ points with a flat tangent cone is $ (m-2) $-rectifiable. This complements the thorough structural analysis of the singularities of area-minimizing hypersurfaces modulo $ p $ that
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Constant Mean Curvature Hypersurfaces in Anti-de Sitter Space Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-02-29 Enrico Trebeschi
We study entire spacelike constant mean curvature hypersurfaces in Anti-de Sitter space of any dimension. First, we give a classification result with respect to their asymptotic boundary, namely we show that every admissible sphere $\Lambda $ is the boundary of a unique such hypersurface, for any given value $H$ of the mean curvature. We also demonstrate that, as $H$ varies in $\mathbb {R}$, these
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Effective Density of Non-Degenerate Random Walks on Homogeneous Spaces Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-02-29 Wooyeon Kim, Constantin Kogler
We prove effective density of random walks on homogeneous spaces, assuming that the underlying measure is supported on matrices generating a dense subgroup and having algebraic entries. The main novelty is an argument passing from high dimension to effective equidistribution in the setting of random walks on homogeneous spaces, exploiting the spectral gap of the associated convolution operator.
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Shuffle Algebras and Their Integral Forms: Specialization Map Approach in Types B n and G 2 Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-02-27 Yue Hu, Alexander Tsymbaliuk
We construct a family of PBWD (Poincaré-Birkhoff-Witt-Drinfeld) bases for the positive subalgebras of quantum loop algebras of type $B_{n}$ and $G_{2}$, as well as their Lusztig and RTT (for type $B_{n}$ only) integral forms, in the new Drinfeld realization. We also establish a shuffle algebra realization of these ${\mathbb {Q}}(v)$-algebras (proved earlier in [26] by completely different tools) and
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Earthquake Theorem for Cluster Algebras of Finite Type Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-02-27 Takeru Asaka, Tsukasa Ishibashi, Shunsuke Kano
We introduce a cluster algebraic generalization of Thurston’s earthquake map for the cluster algebras of finite type, which we call the cluster earthquake map. It is defined by gluing exponential maps, which is modeled after the earthquakes along ideal arcs. We prove an analogue of the earthquake theorem, which states that the cluster earthquake map gives a homeomorphism between the spaces of $\mathbb
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Operator Space Complexification Transfigured Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-02-26 David P Blecher, Mehrdad Kalantar
Given a finite group $G$, a central subgroup $H$ of $G$, and an operator space $X$ equipped with an action of $H$ by complete isometries, we construct an operator space $X_{G}$ equipped with an action of $G$ that is unique under a “reasonable” condition. This generalizes the operator space complexification $X_{c}$ of $X$. As a linear space $X_{G}$ is the space obtained from inducing the representation
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Simple Unbalanced Optimal Transport Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-02-26 Boris Khesin, Klas Modin, Luke Volk
We introduce and study a simple model capturing the main features of unbalanced optimal transport. It is based on equipping the conical extension of the group of all diffeomorphisms with a natural metric, which allows a Riemannian submersion to the space of volume forms of arbitrary total mass. We describe its finite-dimensional version and present a concise comparison study of the geometry, Hamiltonian
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Cocycle Twisting of Semidirect Products and Transmutation Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-02-23 Erik Habbestad, Sergey Neshveyev
We apply Majid’s transmutation procedure to Hopf algebra maps $H \to {{\mathbb {C}}}[T]$, where $T$ is a compact abelian group, and explain how this construction gives rise to braided Hopf algebras over quotients of $T$ by subgroups that are cocentral in $H$. This allows us to unify and generalize a number of recent constructions of braided compact quantum groups, starting from the braided $SU_{q}(2)$
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Picard Groups of Some Quot Schemes Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-02-23 Chandranandan Gangopadhyay, Ronnie Sebastian
Let $C$ be a smooth projective curve over the field of complex numbers ${\mathbb{C}}$ of genus $g(C)>0$. Let $E$ be a locally free sheaf on $C$ of rank $r$ and degree $e$. Let $\mathcal{Q}:=\textrm{Quot}_{C/{\mathbb{C}}}(E,k,d)$ denote the Quot scheme of quotients of $E$ of rank $k$ and degree $d$. For $k>0$ and $d\gg 0$, we compute the Picard group of $\mathcal{Q}$.
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Monotonicity of the p-Green Functions Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-02-23 Pak-Yeung Chan, Jianchun Chu, Man-Chun Lee, Tin-Yau Tsang
On a complete $p$-nonparabolic $3$-dimensional manifold with non-negative scalar curvature and vanishing second homology, we establish a sharp monotonicity formula for the proper $p$-Green function along its level sets for $1
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Winding Number, Density of States, and Acceleration Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-02-23 Xueyin Wang, Zhenfu Wang, Jiangong You, Qi Zhou
Winding number and density of states are two fundamental physical quantities for non-self-adjoint quasi-periodic Schrödinger operators, which reflect the asymptotic distribution of zeros of the characteristic determinants of the truncated operators under Dirichlet boundary condition, with respect to complexified phase and the energy, respectively. We will prove that the winding number is in fact Avila’s
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On Uniqueness in Steiner Problem Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-02-22 Mikhail Basok, Danila Cherkashin, Nikita Rastegaev, Yana Teplitskaya
We prove that the set of $n$-point configurations for which the solution to the planar Steiner problem is not unique has the Hausdorff dimension at most $2n-1$ (as a subset of $\mathbb{R}^{2n}$). Moreover, we show that the Hausdorff dimension of the set of $n$-point configurations for which at least two locally minimal trees have the same length is also at most $2n-1$. The methods we use essentially
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Noncommutative Poisson Boundaries, Ultraproducts, and Entropy Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-02-22 Shuoxing Zhou
We construct the noncommutative Poisson boundaries of tracial von Neumann algebras through the ultraproducts of von Neumann algebras. As an application of this result, we complete the proof of Kaimanovich-Vershik’s fundamental theorems regarding noncommutative entropy. We also prove the Amenability-Trivial Boundary equivalence and Choquet-Deny-Type I equivalence for tracial von Neumann algebras.
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Examples of Non-Rigid, Modular Vector Bundles on Hyperkähler Manifolds Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-02-21 Enrico Fatighenti
We exhibit examples of slope-stable and modular vector bundles on a hyperkähler manifold of K3$^{[2]}$-type, which move in a 20-dimensional family and study their algebraic properties. These are obtained by performing standard linear algebra constructions on the examples studied by O’Grady of (rigid) modular bundles on the Fano varieties of lines of a general cubic four-fold and the Debarre–Voisin
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The (Self-Similar, Variational) Rolling Stones Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-02-21 Dylan Langharst, Jacopo Ulivelli
The interplay between variational functionals and the Brunn–Minkowski Theory is a well-established phenomenon widely investigated in the last thirty years. In this work, we prove the existence of solutions to the even logarithmic Minkowski problems arising from variational functionals, such as the first eigenvalue of the Laplacian and the torsional rigidity. In particular, we lay down a blueprint showing
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Effective Morphisms and Quotient Stacks Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-02-17 Andrea Di Lorenzo, Giovanni Inchiostro
We give a valuative criterion for when a smooth algebraic stack with a separated good moduli space is the quotient of a separated Deligne–Mumford stack by a torus. For doing so, we introduce a new class of morphisms, the effective morphisms, which are a generalization of separated morphisms.
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Trend to Equilibrium for Flows With Random Diffusion Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-02-17 Shrey Aryan, Matthew Rosenzweig, Gigliola Staffilani
Motivated by the possibility of noise to cure equations of finite-time blowup, the recent work [ 90] by the second and third named authors showed that with quantifiable high probability, random diffusion restores global existence for a large class of active scalar equations in arbitrary dimension with possibly singular velocity fields. This class includes Hamiltonian flows, such as the SQG equation
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Nodal Decompositions of a Symmetric Matrix Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-02-17 Theo McKenzie, John Urschel
Analyzing nodal domains is a way to discern the structure of eigenvectors of operators on a graph. We give a new definition extending the concept of nodal domains to arbitrary signed graphs, and therefore to arbitrary symmetric matrices. We show that for an arbitrary symmetric matrix, a positive fraction of eigenbases satisfy a generalized version of known nodal bounds for un-signed (that is classical)
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A Non-Symmetric Kesten Criterion and Ratio Limit Theorem for Random Walks on Amenable Groups Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-02-17 Rhiannon Dougall, Richard Sharp
We consider random walks on countable groups. A celebrated result of Kesten says that the spectral radius of a symmetric walk (whose support generates the group as a semigroup) is equal to one if and only if the group is amenable. We give an analogue of this result for walks that are not symmetric. We also conclude a ratio limit theorem for amenable groups.
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Exceptional Set Estimate Through Brascamp–Lieb Inequality Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-02-09 Shengwen Gan
Fix integers $1\le k
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Maximal Polarization for Periodic Configurations on the Real Line Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-02-07 Markus Faulhuber, Stefan Steinerberger
We prove that among all 1-periodic configurations $\Gamma $ of points on the real line $\mathbb{R}$ the quantities $\min _{x \in \mathbb{R}} \sum _{\gamma \in \Gamma } e^{- \pi \alpha (x - \gamma )^{2}}$ and $\max _{x \in \mathbb{R}} \sum _{\gamma \in \Gamma } e^{- \pi \alpha (x - \gamma )^{2}}$ are maximized and minimized, respectively, if and only if the points are equispaced and whenever the number
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Tamely Ramified Geometric Langlands Correspondence in Positive Characteristic Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-02-05 Shiyu Shen
We prove a version of the tamely ramified geometric Langlands correspondence in positive characteristic for $GL_{n}(k)$, where $k$ is an algebraically closed field of characteristic $p> n$. Let $X$ be a smooth projective curve over $k$ with marked points, and fix a parabolic subgroup of $GL_{n}(k)$ at each marked point. We denote by $\operatorname{Bun}_{n,P}$ the moduli stack of (quasi-)parabolic vector
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An Analogue of Ladder Representations for Classical Groups Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-02-05 Hiraku Atobe
In this paper, we introduce a notion of ladder representations for split odd special orthogonal groups and symplectic groups over a non-archimedean local field of characteristic zero. This is a natural class in the admissible dual, which contains both strongly positive discrete series representations and irreducible representations with irreducible $A$-parameters. We compute Jacquet modules and the
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Interlacing Polynomial Method for the Column Subset Selection Problem Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-01-29 Jian-Feng Cai, Zhiqiang Xu, Zili Xu
This paper investigates the spectral norm version of the column subset selection problem. Given a matrix $\textbf{A}\in \mathbb{R}^{n\times d}$ and a positive integer $k\leq \textrm{rank}(\textbf{A})$, the objective is to select exactly $k$ columns of $\textbf{A}$ that minimize the spectral norm of the residual matrix after projecting $\textbf{A}$ onto the space spanned by the selected columns. We
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Positive Mass Theorems for Spin Initial Data Sets With Arbitrary Ends and Dominant Energy Shields Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-01-29 Simone Cecchini, Martin Lesourd, Rudolf Zeidler
We prove a positive mass theorem for spin initial data sets $(M,g,k)$ that contain an asymptotically flat end and a shield of dominant energy (a subset of $M$ on which the dominant energy scalar $\mu -|J|$ has a positive lower bound). In a similar vein, we show that for an asymptotically flat end $\mathcal{E}$ that violates the positive mass theorem (i.e., $\textrm{E} < |\textrm{P}|$), there exists