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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
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Non-Strict Plurisubharmonicity of Energy on Teichmüller Space Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-01-29 Ognjen Tošić
For an irreducible representation $\rho :\pi _{1}(\Sigma _{g})\to \textrm{GL}(n,\mathbb{C})$, there is an energy functional $\textrm{E}_{\rho }: {{\mathcal{T}}}_{g}\to \mathbb{R}$, defined on Teichmüller space by taking the energy of the associated equivariant harmonic map into the symmetric space $\textrm{GL}(n,\mathbb{C})/\textrm{U}(n)$. It follows from a result of Toledo that $\textrm{E}_{\rho }$
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Bethe Subalgebras in Antidominantly Shifted Yangians Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-01-26 Vasily Krylov, Leonid Rybnikov
The loop group $G((z^{-1}))$ of a simple complex Lie group $G$ has a natural Poisson structure. We introduce a natural family of Poisson commutative subalgebras $\overline{{\textbf{B}}}(C) \subset{{\mathcal{O}}}(G((z^{-1}))$ depending on the parameter $C\in G$ called classical universal Bethe subalgebras. To every antidominant cocharacter $\mu $ of the maximal torus $T \subset G$, one can associate
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Skew-Orthogonal Polynomials and Pfaff Lattice Hierarchy Associated With an Elliptic Curve Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-01-26 Wei Fu, Shi-Hao Li
Starting with a skew-symmetric inner product over an elliptic curve, we propose the concept of elliptic skew-orthogonal polynomials. Inspired by the Landau–Lifshitz hierarchy and its corresponding time evolutions, we obtain the recurrence relation and the $\tau $-function representation for such a novel class of skew-orthogonal polynomials. Furthermore, a bilinear integral identity is derived through
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Monodromy Kernels for Strata of Translation Surfaces Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-01-25 Riccardo Giannini
The non-hyperelliptic connected components of the strata of translation surfaces are conjectured to be orbifold classifying spaces for some groups commensurable to some mapping class groups. The topological monodromy map of the non-hyperelliptic components projects naturally to the mapping class group of the underlying punctured surface and is an obvious candidate to test commensurability. In the present
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The Incidence Variety Compactification of Strata of d-Differentials in Genus 0 Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-01-25 Duc-Manh Nguyen
Given $d\in \mathbb {Z}_{\geq 2}$, for every $\kappa =(k_{1},\dots ,k_{n}) \in \mathbb {Z}^{n}$ such that $k_{i}\geq 1-d$ and $k_{1}+\dots +k_{n}=-2d$, denote by $\Omega ^{d}\mathcal {M}_{0,n}(\kappa )$ and $\mathbb {P}\Omega ^{d}\mathcal {M}_{0,n}(\kappa )$ the corresponding stratum of $d$-differentials in genus $0$ and its projectivization, respectively. We specify an ideal sheaf of the structure
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The Universe Inside Hall Algebras of Coherent Sheaves on Toric Resolutions Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-01-24 Boris Tsvelikhovskiy
Let $\mathfrak {g}\neq \mathfrak {s}\mathfrak {o}_{8}$ be a simple Lie algebra of type $A,D,E$ with $\widehat {\mathfrak {g}}$ the corresponding affine Kac–Moody algebra and $\mathfrak {n}_{+}\subset \widehat {\mathfrak {g}}$ is the standard positive nilpotent subalgebra. Given $\mathfrak {n}_{+}$ as above, we provide an infinite collection of cyclic finite abelian subgroups of $SL_{3}(\mathbb {C})$
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On the Hessian of Cubic Hypersurfaces Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-01-24 Davide Bricalli, Filippo Francesco Favale, Gian Pietro Pirola
In this paper, we analyze the Hessian locus associated to a general cubic hypersurface, by describing its singular locus and its desingularization for every dimension. The strategy is based on strong connections between the Hessian and the quadrics defined as partial derivatives of the cubic polynomial. In particular, we focus our attention on the singularities of the Hessian hypersurface associated
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Bounds for the Bergman Kernel and the Sup-Norm of Holomorphic Siegel Cusp Forms Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-01-24 Soumya Das, Hariram Krishna
We prove “polynomial in $k$” bounds on the size of the Bergman kernel for the space of holomorphic Siegel cusp forms of degree $n$ and weight $k$. When $n=1,2$ our bounds agree with the conjectural bounds, while the lower bounds match for all $n \ge 1$. For an $L^{2}$-normalized Siegel cusp form $F$ of degree $2$, our bound for its sup-norm is $O_{\epsilon } (k^{9/4+\epsilon })$. Further, we show that
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Recurrent Subspaces in Banach Spaces Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-01-22 Antoni López-Martínez
We study the spaceability of the set of recurrent vectors $\text{Rec}(T)$ for an operator $T:X\longrightarrow X$ on a Banach space $X$. In particular, we find sufficient conditions for a quasi-rigid operator to have a recurrent subspace; when $X$ is a complex Banach space, we show that having a recurrent subspace is equivalent to the fact that the essential spectrum of the operator intersects the closed
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Faithfully Flat Descent of Quasi-Coherent Complexes on Rigid Analytic Varieties via Condensed Mathematics Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-01-18 Yutaro Mikami
Faithfully flat descent of pseudo-coherent complexes in rigid geometry was proved by Mathew. In this paper, we generalize the result of Mathew to solid quasi-coherent complexes on rigid analytic varieties, which have been introduced by Clausen and Scholze by means of condensed mathematics.
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L p -Minkowski Problem Under Curvature Pinching Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-01-17 Mohammad N Ivaki, Emanuel Milman
Let $K$ be a smooth, origin-symmetric, strictly convex body in ${\mathbb{R}}^{n}$. If for some $\ell \in \textrm{GL}(n,{\mathbb{R}})$, the anisotropic Riemannian metric $\frac{1}{2}D^{2} \left \Vert \cdot \right \Vert_{\ell K}^{2}$, encapsulating the curvature of $\ell K$, is comparable to the standard Euclidean metric of ${\mathbb{R}}^{n}$ up-to a factor of $\gamma> 1$, we show that $K$ satisfies
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On Some Birational Invariants of Hyper-Kähler Manifolds Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-01-16 Chenyu Bai
We study in this article three birational invariants of projective hyper-Kähler manifolds: the degree of irrationality, the fibering gonality, and the fibering genus. We first improve the lower bound in a recent result of Voisin saying that the fibering genus of a Mumford–Tate very general projective hyper-Kähler manifold is bounded from below by a constant depending on its dimension and the second
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Burau Representation of Braid Groups and q-Rationals Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-01-15 Sophie Morier-Genoud, Valentin Ovsienko, Alexander P Veselov
We establish a link between the new theory of $q$-deformed rational numbers and the classical Burau representation of the braid group ${\mathcal {B}}_{3}$. We apply this link to the open problem of classification of faithful complex specializations of this representation. As a result we provide an answer to this problem in terms of the singular set of the $q$-rationals and prove the faithfulness of
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The Theory of the Entire Algebraic Functions Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-01-15 Taylor Dupuy, Ehud Hrushovski
Let $A$ be the integral closure of the ring of polynomials ${{\mathbb {C}}}[t]$, within the field of algebraic functions in one variable. We show that $A$ interprets the ring of integers. This contrasts with the analogue for finite fields, proved to have a decidable theory in [12] and [4].
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Stability Analysis of Two-Dimensional Ideal Flows With Applications to Viscous Fluids and Plasmas Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-01-12 Diogo Arsénio, Haroune Houamed
We are interested in the stability analysis of two-dimensional incompressible inviscid fluids. Specifically, we revisit a known recent result on the stability of Yudovich’s solutions to the incompressible Euler equations in $L^{\infty }([0,T];H^{1})$ by providing a new approach to its proof based on the idea of compactness extrapolation and by extending it to the whole plane. This new method of proof
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An Inverse Spectral Problem for Non-Self-Adjoint Jacobi Matrices Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-01-12 Alexander Pushnitski, František Štampach
We consider the class of bounded symmetric Jacobi matrices $J$ with positive off-diagonal elements and complex diagonal elements. With each matrix $J$ from this class, we associate the spectral data, which consists of a pair $(\nu ,\psi )$. Here $\nu $ is the spectral measure of $|J|=\sqrt {J^{*}J}$ and $\psi $ is a phase function on the real line satisfying $|\psi |\leq 1$ almost everywhere with respect
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Index of Minimal Hypersurfaces in Real Projective Spaces Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-01-10 Shuli Chen
We prove that for an embedded unstable one-sided minimal hypersurface of the $(n+1)$-dimensional real projective space, the Morse index is at least $n+2$, and this bound is attained by the cubic isoparametric minimal hypersurfaces. We also show that there exist closed embedded two-sided minimal surfaces in the 3-dimensional real projective space of each odd index by computing the index of the Lawson
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The Twist for Electrical Networks and the Inverse Problem Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-01-10 Terrence George
We construct an electrical-network version of the twist map for the positive Grassmannian, and use it to solve the inverse problem of recovering conductances from the response matrix. Each conductance is expressed as a biratio of Pfaffians as in the inverse map of Kenyon and Wilson; however, our Pfaffians are the more canonical $B$ variables instead of their tripod variables, and are coordinates on
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Generalized Chromatic Functions Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-01-09 Farid Aliniaeifard, Shu Xiao Li, Stephanie van Willigenburg
We define vertex-colourings for edge-partitioned digraphs, which unify the theory of $P$-partitions and proper vertex-colourings of graphs. We use our vertex-colourings to define generalized chromatic functions, which merge the chromatic symmetric and quasisymmetric functions of graphs and generating functions of $P$-partitions. Moreover, numerous classical bases of symmetric and quasisymmetric functions
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Equivariant K-Homology and K-Theory for Some Discrete Planar Affine Groups Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-01-09 Ramon Flores, Sanaz Pooya, Alain Valette
We consider the semi-direct products $G={\mathbb{Z}}^{2}\rtimes GL_{2}({\mathbb{Z}}), {\mathbb{Z}}^{2}\rtimes SL_{2}({\mathbb{Z}})$, and ${\mathbb{Z}}^{2}\rtimes \Gamma (2)$ (where $\Gamma (2)$ is the congruence subgroup of level 2). For each of them, we compute both sides of the Baum–Connes conjecture, namely the equivariant $K$-homology of the classifying space $\underline{E}G$ for proper actions
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A Finite Topological Type Theorem for Open Manifolds with Non-negative Ricci Curvature and Almost Maximal Local Rewinding Volume Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-01-04 HongZhi Huang
In this paper, we present finite topological type theorems for open manifolds with non-negative Ricci curvature, under almost maximal local rewinding volume. Unlike previous related research, our theorems remove the constraints of sectional curvature or conjugate radius, which were crucial additional assumptions on metric regularity in prior results. Notably, our settings do not necessarily satisfy
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Projective Transformations of Convex Bodies and Volume Product Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-01-04 Florent Balacheff, Gil Solanes, Kroum Tzanev
In this paper, we study certain variational aspects of the volume product functional restricted to the space of small projective deformations of a fixed convex body. In doing so, we provide a short proof of a theorem by Klartag: a strong version of the slicing conjecture implies the non-symmetric Mahler conjecture. We also exhibit an interesting family of critical convex bodies in dimension $2$ containing
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Multiplicities and Dimensions in Enveloping Tensor Categories Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-01-03 Friedrich Knop
In a previous paper, semisimple tensor categories were constructed from certain regular Mal’cev categories. In this paper, we calculate the tensor product multiplicities and the categorical dimensions of the simple objects. This yields also the Grothendieck ring. The main tool is the subquotient decomposition of the generating objects.
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Formality in the Deligne-Langlands Correspondence Int. Math. Res. Notices (IF 1.0) Pub Date : 2024-01-03 Jonas Antor
The Deligne-Langlands correspondence parametrizes irreducible representations of the affine Hecke algebra $\mathcal{H}^{\operatorname{aff}}$ by certain perverse sheaves. We show that this can be lifted to an equivalence of triangulated categories. More precisely, we construct for each central character $\chi $ of $\mathcal{H}^{\operatorname{aff}}$ an equivalence of triangulated categories between a
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Mean Field Approximations via Log-Concavity Int. Math. Res. Notices (IF 1.0) Pub Date : 2023-12-22 Daniel Lacker, Sumit Mukherjee, Lane Chun Yeung
We propose a new approach to deriving quantitative mean field approximations for any probability measure $P$ on $\mathbb {R}^{n}$ with density proportional to $e^{f(x)}$, for $f$ strongly concave. We bound the mean field approximation for the log partition function $\log \int e^{f(x)}dx$ in terms of $\sum _{i \neq j}\mathbb {E}_{Q^{*}}|\partial _{ij}f|^{2}$, for a semi-explicit probability measure
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Rigidity, Tensegrity, and Reconstruction of Polytopes Under Metric Constraints Int. Math. Res. Notices (IF 1.0) Pub Date : 2023-12-22 Martin Winter
We conjecture that a convex polytope is uniquely determined up to isometry by its edge-graph, edge lengths and the collection of distances of its vertices to some arbitrary interior point, across all dimensions and all combinatorial types. We conjecture even stronger that for two polytopes $P\subset {\mathbb {R}}^{d}$ and $Q\subset {\mathbb {R}}^{e}$ with the same edge-graph it is not possible that
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Prasad’s Conjecture About Dualizing Involutions Int. Math. Res. Notices (IF 1.0) Pub Date : 2023-12-19 Prashant Arote, Manish Mishra
Let $G$ be a connected reductive group defined over a finite field ${\mathbb{F}}_{q}$ with corresponding Frobenius $F$. Let $\iota _{G}$ denote the duality involution defined by D. Prasad under the hypothesis $2\textrm{H}^{1}(F,Z(G))=0$, where $Z(G)$ denotes the center of $G$. We show that for each irreducible character $\rho $ of $G^{F}$, the involution $\iota _{G}$ takes $\rho $ to its dual $\rho
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Perfect t-Embeddings of Uniformly Weighted Aztec Diamonds and Tower Graphs Int. Math. Res. Notices (IF 1.0) Pub Date : 2023-12-19 Tomas Berggren, Matthew Nicoletti, Marianna Russkikh
In this work we study a sequence of perfect t-embeddings of uniformly weighted Aztec diamonds. We show that these perfect t-embeddings can be used to prove convergence of gradients of height fluctuations to those of the Gaussian free field. In particular, we provide a first proof of the existence of a model satisfying all conditions of the main theorem of [9]. This confirms the prediction of [10].
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Corrigendum to “K-theoretic Characterization of C*-algebras with Approximately Inner Flip” Int. Math. Res. Notices (IF 1.0) Pub Date : 2023-12-18 Dominic Enders, André Schemaitat, Aaron Tikuisis
An error in the original paper is identified and corrected. The $\textrm {C}^{\ast }$-algebras with approximately inner flip, which satisfy the UCT, are identified (and turn out to be fewer than what is claimed in the original paper). The action of the flip map on K-theory turns out to be more subtle, involving a minus sign in certain components. To this end, we introduce new geometric resolutions
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Fourier Transform from the Symmetric Square Representation of PGL2 and SL2 Int. Math. Res. Notices (IF 1.0) Pub Date : 2023-12-18 Gérard Laumon, Emmanuel Letellier
Let $G$ be a connected reductive group over $\overline{{\mathbb{F}}}_{q}$ and let $\rho ^{\vee }:G^{\vee }\rightarrow \mathrm{GL}_{n}$ be an algebraic representation of the dual group $G^{\vee }$. Assuming that $G$ and $\rho ^{\vee }$ are defined over ${\mathbb{F}}_{q}$, Braverman and Kazhdan defined an operator on the space ${{\mathcal{C}}}(G({\mathbb{F}}_{q}))$ of complex valued functions on $G({\mathbb{F}}_{q})$