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Monodromy of the Casimir connection of a symmetrisable Kac–Moody algebra Invent. math. (IF 3.1) Pub Date : 2024-03-14 Andrea Appel, Valerio Toledano Laredo
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Monoidal categorification and quantum affine algebras II Invent. math. (IF 3.1) Pub Date : 2024-03-12 Masaki Kashiwara, Myungho Kim, Se-jin Oh, Euiyong Park
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Demazure crystals and the Schur positivity of Catalan functions Invent. math. (IF 3.1) Pub Date : 2024-03-08 Jonah Blasiak, Jennifer Morse, Anna Pun
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Stability of the Faber-Krahn inequality for the short-time Fourier transform Invent. math. (IF 3.1) Pub Date : 2024-03-01 Jaime Gómez, André Guerra, João P. G. Ramos, Paolo Tilli
We prove a sharp quantitative version of the Faber–Krahn inequality for the short-time Fourier transform (STFT). To do so, we consider a deficit \(\delta (f;\Omega )\) which measures by how much the STFT of a function \(f\in L^{2}(\mathbb{R})\) fails to be optimally concentrated on an arbitrary set \(\Omega \subset \mathbb{R}^{2}\) of positive, finite measure. We then show that an optimal power of
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Uniform negative immersions and the coherence of one-relator groups Invent. math. (IF 3.1) Pub Date : 2024-02-29 Larsen Louder, Henry Wilton
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The largest prime factor of $n^{2}+1$ and improvements on subexponential $ABC$ Invent. math. (IF 3.1) Pub Date : 2024-02-26 Hector Pasten
We combine transcendental methods and the modular approaches to the \(ABC\) conjecture to show that the largest prime factor of \(n^{2}+1\) is at least of size \((\log _{2} n)^{2}/\log _{3}n\) where \(\log _{k}\) is the \(k\)-th iterate of the logarithm. This gives a substantial improvement on the best available estimates, which are essentially of size \(\log _{2} n\) going back to work of Chowla in
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Virasoro constraints for moduli of sheaves and vertex algebras Invent. math. (IF 3.1) Pub Date : 2024-02-23 Arkadij Bojko, Woonam Lim, Miguel Moreira
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A $p$ -adic arithmetic inner product formula Invent. math. (IF 3.1) Pub Date : 2024-02-23
Abstract Fix a prime number \(p\) and let \(E/F\) be a CM extension of number fields in which \(p\) splits relatively. Let \(\pi \) be an automorphic representation of a quasi-split unitary group of even rank with respect to \(E/F\) such that \(\pi \) is ordinary above \(p\) with respect to the Siegel parabolic subgroup. We construct the cyclotomic \(p\) -adic \(L\) -function of \(\pi \) , and a certain
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Existence of harmonic maps and eigenvalue optimization in higher dimensions Invent. math. (IF 3.1) Pub Date : 2024-02-21 Mikhail Karpukhin, Daniel Stern
We prove the existence of nonconstant harmonic maps of optimal regularity from an arbitrary closed manifold \((M^{n},g)\) of dimension \(n>2\) to any closed, non-aspherical manifold \(N\) containing no stable minimal two-spheres. In particular, this gives the first general existence result for harmonic maps from higher-dimensional manifolds to a large class of positively curved targets. In the special
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A prismatic approach to crystalline local systems Invent. math. (IF 3.1) Pub Date : 2024-02-19 Haoyang Guo, Emanuel Reinecke
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Wilson spaces, snaith constructions, and elliptic orientations Invent. math. (IF 3.1) Pub Date : 2024-02-15 Hood Chatham, Jeremy Hahn, Allen Yuan
We construct a canonical family of even periodic \(\mathbb{E}_{\infty}\)-ring spectra, with exactly one member of the family for every prime \(p\) and chromatic height \(n\). At height 1 our construction is due to Snaith, who built complex \(K\)-theory from \(\mathbb{CP}^{\infty}\). At height 2 we replace \(\mathbb{CP}^{\infty}\) with a \(p\)-local retract of \(\mathrm{BU} \langle 6 \rangle \), producing
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SRB measures for $C^{\infty }$ surface diffeomorphisms Invent. math. (IF 3.1) Pub Date : 2024-02-05
Abstract A \(C^{\infty }\) smooth surface diffeomorphism admits an SRB measure if and only if the set \(\{ x, \ \limsup _{n}\frac{1}{n}\log \|d_{x}f^{n}\|>0\}\) has positive Lebesgue measure. Moreover the basins of the ergodic SRB measures are covering this set Lebesgue almost everywhere. We also obtain similar results for \(C^{r}\) surface diffeomorphisms with \(+\infty >r>1\) .
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Fano 4-folds with $b_{2}>12$ are products of surfaces Invent. math. (IF 3.1) Pub Date : 2024-02-05 C. Casagrande
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A phantom on a rational surface Invent. math. (IF 3.1) Pub Date : 2023-12-21 Johannes Krah
We construct a non-full exceptional collection of maximal length consisting of line bundles on the blow-up of the projective plane in 10 general points. As a consequence, the orthogonal complement of this collection is a universal phantom category. This provides a counterexample to a conjecture of Kuznetsov and to a conjecture of Orlov.
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The time-like minimal surface equation in Minkowski space: low regularity solutions Invent. math. (IF 3.1) Pub Date : 2023-12-07 Albert Ai, Mihaela Ifrim, Daniel Tataru
It has long been conjectured that for nonlinear wave equations that satisfy a nonlinear form of the null condition, the low regularity well-posedness theory can be significantly improved compared to the sharp results of Smith-Tataru for the generic case. The aim of this article is to prove the first result in this direction, namely for the time-like minimal surface equation in the Minkowski space-time
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Scalar curvature rigidity of convex polytopes Invent. math. (IF 3.1) Pub Date : 2023-11-29 Simon Brendle
We prove a scalar curvature rigidity theorem for convex polytopes. The proof uses the Fredholm theory for Dirac operators on manifolds with boundary. A variant of a theorem of Fefferman and Phong plays a central role in our analysis.
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Derivation of Kubo’s formula for disordered systems at zero temperature Invent. math. (IF 3.1) Pub Date : 2023-11-28 Wojciech De Roeck, Alexander Elgart, Martin Fraas
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Higher Siegel–Weil formula for unitary groups: the non-singular terms Invent. math. (IF 3.1) Pub Date : 2023-11-27 Tony Feng, Zhiwei Yun, Wei Zhang
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Coherent Springer theory and the categorical Deligne-Langlands correspondence Invent. math. (IF 3.1) Pub Date : 2023-11-06 David Ben-Zvi, Harrison Chen, David Helm, David Nadler
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On the distribution of the Hodge locus Invent. math. (IF 3.1) Pub Date : 2023-11-03 Gregorio Baldi, Bruno Klingler, Emmanuel Ullmo
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Localization crossover for the continuous Anderson Hamiltonian in 1-d Invent. math. (IF 3.1) Pub Date : 2023-11-03 Laure Dumaz, Cyril Labbé
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Subgroups of hyperbolic groups, finiteness properties and complex hyperbolic lattices Invent. math. (IF 3.1) Pub Date : 2023-10-12 Claudio Llosa Isenrich, Pierre Py
We prove that in a cocompact complex hyperbolic arithmetic lattice \(\Gamma < {\mathrm{PU}}(m,1)\) of the simplest type, deep enough finite index subgroups admit plenty of homomorphisms to ℤ with kernel of type \(\mathscr{F}_{m-1}\) but not of type \(\mathscr{F}_{m}\). This provides many finitely presented non-hyperbolic subgroups of hyperbolic groups and answers an old question of Brady. Our method
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The anisotropic Bernstein problem Invent. math. (IF 3.1) Pub Date : 2023-10-04 Connor Mooney, Yang Yang
We construct nonlinear entire anisotropic minimal graphs over \(\mathbb{R}^{4}\), completing the solution to the anisotropic Bernstein problem. The examples we construct have a variety of growth rates, and our approach both generalizes to higher dimensions and recovers and elucidates known examples of nonlinear entire minimal graphs over \(\mathbb{R}^{n},\, n \geq 8\).
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Character levels and character bounds for finite classical groups Invent. math. (IF 3.1) Pub Date : 2023-09-29 Robert M. Guralnick, Michael Larsen, Pham Huu Tiep
The main results of the paper develop a level theory and establish strong character bounds for finite classical groups, in the case that the centralizer of the element has small order compared to \(|G|\) in a logarithmic sense.
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On the birational section conjecture with strong birationality assumptions Invent. math. (IF 3.1) Pub Date : 2023-09-26 Giulio Bresciani
Let \(X\) be a curve over a field \(k\) finitely generated over ℚ and \(t\) an indeterminate. We prove that, if \(s\) is a section of \(\pi _{1}(X)\to \operatorname{Gal}(k)\) such that the base change \(s_{k(t)}\) is birationally liftable, then \(s\) comes from geometry. As a consequence we prove that the section conjecture is equivalent to the cuspidalization of all sections over all finitely generated
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Non-reductive geometric invariant theory and hyperbolicity Invent. math. (IF 3.1) Pub Date : 2023-09-26 Gergely Bérczi, Frances Kirwan
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Moment maps and cohomology of non-reductive quotients Invent. math. (IF 3.1) Pub Date : 2023-09-26 Gergely Bérczi, Frances Kirwan
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Nonuniformly elliptic Schauder theory Invent. math. (IF 3.1) Pub Date : 2023-09-27 Cristiana De Filippis, Giuseppe Mingione
Local Schauder theory holds in the nonuniformly elliptic setting. Specifically, first derivatives of solutions to nonuniformly elliptic problems are locally Hölder continuous if so are their coefficients.
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A Chabauty–Coleman bound for surfaces Invent. math. (IF 3.1) Pub Date : 2023-09-20 Jerson Caro, Hector Pasten
Building on work by Chabauty from 1941, Coleman proved in 1985 an explicit bound for the number of rational points of a curve \(C\) of genus \(g\ge 2\) defined over a number field \(F\), with Jacobian of rank at most \(g-1\). Namely, in the case \(F=\mathbb{Q}\), if \(p>2g\) is a prime of good reduction, then the number of rational points of \(C\) is at most the number of \(\mathbb{F}_{p}\)-points
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Existence of moduli spaces for algebraic stacks Invent. math. (IF 3.1) Pub Date : 2023-08-22 Jarod Alper, Daniel Halpern-Leistner, Jochen Heinloth
We provide necessary and sufficient conditions for when an algebraic stack admits a good moduli space and prove a semistable reduction theorem for points of algebraic stacks equipped with a \(\Theta \)-stratification. These results provide a generalization of the Keel–Mori theorem to moduli problems whose objects have positive dimensional automorphism groups and give criteria on the moduli problem
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One dimensional representations of finite $W$ -algebras, Dirac reduction and the orbit method Invent. math. (IF 3.1) Pub Date : 2023-08-21 Lewis Topley
In this paper we study the variety of one dimensional representations of a finite \(W\)-algebra attached to a classical Lie algebra, giving a precise description of the dimensions of the irreducible components. We apply this to prove a conjecture of Losev describing the image of his orbit method map. In order to do so we first establish new Yangian-type presentations of semiclassical limits of the
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Evaluating the wild Brauer group Invent. math. (IF 3.1) Pub Date : 2023-08-08 Martin Bright, Rachel Newton
Classifying elements of the Brauer group of a variety \(X\) over a \(p\)-adic field by the \(p\)-adic accuracy needed to evaluate them gives a filtration on \(\operatorname{Br}X\). We relate this filtration to that defined by Kato’s Swan conductor. The refined Swan conductor controls how the evaluation maps vary on \(p\)-adic discs: this provides a geometric characterisation of the refined Swan conductor
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Rigidity of Kleinian groups via self-joinings Invent. math. (IF 3.1) Pub Date : 2023-08-02 Dongryul M. Kim, Hee Oh
Let \(\Gamma <\operatorname{PSL}_{2}(\mathbb{C})\simeq \operatorname{Isom}^{+}( \mathbb{H}^{3})\) be a finitely generated non-Fuchsian Kleinian group whose ordinary set \(\Omega =\mathbb{S}^{2}-\Lambda \) has at least two components. Let \(\rho : \Gamma \to \operatorname{PSL}_{2}(\mathbb{C})\) be a faithful discrete non-Fuchsian representation with boundary map \(f:\Lambda \to \mathbb{S}^{2}\) on the
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Cyclic quadrilaterals and smooth Jordan curves Invent. math. (IF 3.1) Pub Date : 2023-08-02 Joshua Evan Greene, Andrew Lobb
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Banach property (T) for $\mathrm{SL}_{n} (\mathbb{Z})$ and its applications Invent. math. (IF 3.1) Pub Date : 2023-07-31 Izhar Oppenheim
We prove that a large family of higher rank simple Lie groups (including \(\mathrm{SL}_{n} (\mathbb{R})\) for \(n \geq 3\)) and their lattices have Banach property (T) with respect to all super-reflexive Banach spaces. Two consequences of this result are: First, we deduce Banach fixed point properties with respect to all super-reflexive Banach spaces for a large family of higher rank simple Lie groups
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A proof of the Kudla–Rapoport conjecture for Krämer models Invent. math. (IF 3.1) Pub Date : 2023-07-21 Qiao He, Chao Li, Yousheng Shi, Tonghai Yang
We prove the Kudla–Rapoport conjecture for Krämer models of unitary Rapoport–Zink spaces at ramified places. It is a precise identity between arithmetic intersection numbers of special cycles on Krämer models and modified derived local densities of hermitian forms. As an application, we relax the local assumptions at ramified places in the arithmetic Siegel–Weil formula for unitary Shimura varieties
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Non-equilibrium large deviations and parabolic-hyperbolic PDE with irregular drift Invent. math. (IF 3.1) Pub Date : 2023-07-19 Benjamin Fehrman, Benjamin Gess
Large deviations of conservative interacting particle systems, such as the zero range process, about their hydrodynamic limit and their respective rate functions lead to the analysis of the skeleton equation; a degenerate parabolic-hyperbolic PDE with irregular drift. We develop a robust well-posedness theory for such PDEs in energy-critical spaces based on concepts of renormalized solutions and the
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The maximal subgroups of the exceptional groups $F_{4}(q)$ , $E_{6}(q)$ and $^{2}\!E_{6}(q)$ and related almost simple groups Invent. math. (IF 3.1) Pub Date : 2023-07-12 David A. Craven
This article produces a complete list of all maximal subgroups of the finite simple groups of type \(F_{4}\), \(E_{6}\) and twisted \(E_{6}\) over all finite fields. Along the way, we determine the collection of Lie primitive almost simple subgroups of the corresponding algebraic groups. We give the stabilizers under the actions of outer automorphisms, from which one can obtain complete information
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Seshadri stratifications and standard monomial theory Invent. math. (IF 3.1) Pub Date : 2023-07-10 Rocco Chirivì, Xin Fang, Peter Littelmann
We introduce the notion of a Seshadri stratification on an embedded projective variety. Such a structure enables us to construct a Newton-Okounkov simplicial complex and a flat degeneration of the projective variety into a union of toric varieties. We show that the Seshadri stratification provides a geometric setup for a standard monomial theory. In this framework, Lakshmibai-Seshadri paths for Schubert
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Matrix concentration inequalities and free probability Invent. math. (IF 3.1) Pub Date : 2023-06-21 Afonso S. Bandeira, March T. Boedihardjo, Ramon van Handel
A central tool in the study of nonhomogeneous random matrices, the noncommutative Khintchine inequality, yields a nonasymptotic bound on the spectral norm of general Gaussian random matrices \(X=\sum _{i} g_{i} A_{i}\) where \(g_{i}\) are independent standard Gaussian variables and \(A_{i}\) are matrix coefficients. This bound exhibits a logarithmic dependence on dimension that is sharp when the matrices
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Zeta morphisms for rank two universal deformations Invent. math. (IF 3.1) Pub Date : 2023-06-15 Kentaro Nakamura
In this article, we construct zeta morphisms for the universal deformations of odd absolutely irreducible two dimensional mod \(p\) Galois representations satisfying some mild assumptions, and prove that our zeta morphisms interpolate Kato’s zeta morphisms for Galois representations associated to Hecke eigen cusp newforms. The existence of such morphisms was predicted by Kato’s generalized Iwasawa
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Algebraicity of higher Green functions at a CM point Invent. math. (IF 3.1) Pub Date : 2023-06-15 Yingkun Li
In this paper, we investigate the algebraic nature of the value of a higher Green function on an orthogonal Shimura variety at a single CM point. This is motivated by a conjecture of Gross and Zagier in the setting of higher Green functions on the product of two modular curves. In the process, we will study analogue of harmonic Maass forms in the setting of Hilbert modular forms, and obtain results
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Large prime gaps and probabilistic models Invent. math. (IF 3.1) Pub Date : 2023-06-14 William Banks, Kevin Ford, Terence Tao
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Gelfand–Kirillov dimension and mod $p$ cohomology for $\operatorname{GL}_{2}$ Invent. math. (IF 3.1) Pub Date : 2023-06-14 Christophe Breuil, Florian Herzig, Yongquan Hu, Stefano Morra, Benjamin Schraen
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The rates of growth in a hyperbolic group Invent. math. (IF 3.1) Pub Date : 2023-06-08 Koji Fujiwara, Zlil Sela
We study the countable set of rates of growth of a hyperbolic group with respect to all its finite generating sets. We prove that the set is well-ordered, and that every real number can be the rate of growth of at most finitely many generating sets up to automorphism of the group. We prove that the ordinal of the set of rates of growth is at least \({\omega _{0}}^{\omega _{0}}\), and in case the group
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Szegő condition, scattering, and vibration of Krein strings Invent. math. (IF 3.1) Pub Date : 2023-06-07 R. Bessonov, S. Denisov
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Irreducibility of random polynomials: general measures Invent. math. (IF 3.1) Pub Date : 2023-06-05 Lior Bary-Soroker, Dimitris Koukoulopoulos, Gady Kozma
Let \(\mu \) be a probability measure on ℤ that is not a Dirac mass and that has finite support. We prove that if the coefficients of a monic polynomial \(f(x)\in \mathbb{Z}[x]\) of degree \(n\) are chosen independently at random according to \(\mu \) while ensuring that \(f(0)\neq 0\), then there is a positive constant \(\theta =\theta (\mu )\) such that \(f(x)\) has no divisors of degree \(\leq \theta
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Pólya’s conjecture for Euclidean balls Invent. math. (IF 3.1) Pub Date : 2023-06-05 Nikolay Filonov, Michael Levitin, Iosif Polterovich, David A. Sher
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Time quasi-periodic vortex patches of Euler equation in the plane Invent. math. (IF 3.1) Pub Date : 2023-05-23 Massimiliano Berti, Zineb Hassainia, Nader Masmoudi
We prove the existence of time quasi-periodic vortex patch solutions of the 2\(d\)-Euler equations in \(\mathbb{R}^{2} \), close to uniformly rotating Kirchhoff elliptical vortices, with aspect ratios belonging to a set of asymptotically full Lebesgue measure. The problem is reformulated into a quasi-linear Hamiltonian equation for a radial displacement from the ellipse. A major difficulty of the KAM
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Banach’s isometric subspace problem in dimension four Invent. math. (IF 3.1) Pub Date : 2023-05-23 Sergei Ivanov, Daniil Mamaev, Anya Nordskova
We prove that if all intersections of a convex body \(B\subset \mathbb{R}^{4}\) with 3-dimensional linear subspaces are linearly equivalent then \(B\) is a centered ellipsoid. This gives an affirmative answer to the case \(n=3\) of the following question by Banach from 1932: Is a normed vector space \(V\) whose \(n\)-dimensional linear subspaces are all isometric, for a fixed \(2 \le n< \dim V\), necessarily
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Compactness theory of the space of Super Ricci flows Invent. math. (IF 3.1) Pub Date : 2023-05-12 Richard H Bamler
We develop a compactness theory for super Ricci flows, which lays the foundations for the partial regularity theory in Bamler (Structure Theory of Non-collapsed Limits of Ricci Flows, arXiv:2009.03243, 2020). Our results imply that any sequence of super Ricci flows of the same dimension that is pointed in an appropriate sense subsequentially converges to a certain type of synthetic flow, called a metric
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Tautological classes of matroids Invent. math. (IF 3.1) Pub Date : 2023-05-03 Andrew Berget, Christopher Eur, Hunter Spink, Dennis Tseng
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On the cost of the bubble set for random interlacements Invent. math. (IF 3.1) Pub Date : 2023-04-28 Alain-Sol Sznitman
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Marked Length Spectral determination of analytic chaotic billiards with axial symmetries Invent. math. (IF 3.1) Pub Date : 2023-04-25 Jacopo De Simoi, Vadim Kaloshin, Martin Leguil
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On convergence of form factor expansions in the infinite volume quantum Sinh-Gordon model in 1+1 dimensions Invent. math. (IF 3.1) Pub Date : 2023-04-25 Karol K. Kozlowski
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Full derivation of the wave kinetic equation Invent. math. (IF 3.1) Pub Date : 2023-04-21 Yu Deng, Zaher Hani
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Distributed algorithms, the Lovász Local Lemma, and descriptive combinatorics Invent. math. (IF 3.1) Pub Date : 2023-04-19 Anton Bernshteyn
In this paper we consider coloring problems on graphs and other combinatorial structures on standard Borel spaces. Our goal is to obtain sufficient conditions under which such colorings can be made well-behaved in the sense of topology or measure. To this end, we show that such well-behaved colorings can be produced using certain powerful techniques from finite combinatorics and computer science. First
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No semistability at infinity for Calabi-Yau metrics asymptotic to cones Invent. math. (IF 3.1) Pub Date : 2023-04-18 Song Sun, Junsheng Zhang
We discover a “no semistability at infinity” phenomenon for complete Calabi-Yau metrics asymptotic to cones, which is proved by eliminating the possible appearance of an intermediate K-semistable cone in the 2-step degeneration theory developed by Donaldson and the first author. It is in sharp contrast to the setting of local singularities of Kähler-Einstein metrics. A byproduct of the proof is a polynomial
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Equal sums in random sets and the concentration of divisors Invent. math. (IF 3.1) Pub Date : 2023-03-29 Kevin Ford, Ben Green, Dimitris Koukoulopoulos