样式： 排序： IF:  GO 导出 标记为已读

Part 1 of Martin’s Conjecture for orderpreserving and measurepreserving functions J. Am. Math. Soc. (IF 3.5) Pub Date : 20240402
Patrick Lutz, Benjamin SiskindMartin’s Conjecture is a proposed classification of the definable functions on the Turing degrees. It is usually divided into two parts, the first of which classifies functions which are not above the identity and the second of which classifies functions which are above the identity. Slaman and Steel proved the second part of the conjecture for Borel functions which are orderpreserving (i.e. which

Algebraic cobordism and a Conner–Floyd isomorphism for algebraic Ktheory J. Am. Math. Soc. (IF 3.5) Pub Date : 20240222
Toni Annala, Marc Hoyois, Ryomei IwasaWe formulate and prove a Conner–Floyd isomorphism for the algebraic Ktheory of arbitrary qcqs derived schemes. To that end, we study a stable ∞ \infty category of non A 1 \mathbb {A}^1 invariant motivic spectra, which turns out to be equivalent to the ∞ \infty category of fundamental motivic spectra satisfying elementary blowup excision, previously introduced by the first and third authors. We

Purity in chromatically localized algebraic 𝐾theory J. Am. Math. Soc. (IF 3.5) Pub Date : 20240201
Markus Land, Akhil Mathew, Lennart Meier, Georg TammeWe prove a purity property in telescopically localized algebraic K K theory of ring spectra: For n ≥ 1 n\geq 1 , the T ( n ) T(n) localization of K ( R ) K(R) only depends on the T ( 0 ) ⊕ ⋯ ⊕ T ( n ) T(0)\oplus \dots \oplus T(n) localization of R R . This complements a classical result of Waldhausen in rational K K theory. Combining our result with work of Clausen–Mathew–Naumann–Noel, one finds

The singular set in the Stefan problem J. Am. Math. Soc. (IF 3.5) Pub Date : 20240126
Alessio Figalli, Xavier RosOton, Joaquim Serra 
The singularity probability of a random symmetric matrix is exponentially small J. Am. Math. Soc. (IF 3.5) Pub Date : 20240119
Marcelo Campos, Matthew Jenssen, Marcus Michelen, Julian SahasrabudheLet A A be drawn uniformly at random from the set of all n × n n\times n symmetric matrices with entries in { − 1 , 1 } \{1,1\} . We show that \[ P ( det ( A ) = 0 ) ⩽ e − c n , \mathbb {P}( \det (A) = 0 ) \leqslant e^{cn}, \] where c > 0 c>0 is an absolute constant, thereby resolving a longstanding conjecture.

No infinite spin for planar total collision J. Am. Math. Soc. (IF 3.5) Pub Date : 20240118
Richard Moeckel, Richard MontgomeryThe infinite spin problem is an old problem concerning the rotational behavior of total collision orbits in the nbody problem. It has long been known that when a solution tends to total collision then its normalized configuration curve must converge to the set of normalized central configurations. In the planar nbody problem every normalized configuration determines a circle of rotationally equivalent

Convergence of exclusion processes and the KPZ equation to the KPZ fixed point J. Am. Math. Soc. (IF 3.5) Pub Date : 20220308
Jeremy Quastel,Sourav SarkarWe show that under the 1:2:3 scaling, critically probing large space and time, the height function of finite range asymmetric exclusion processes and the KardarParisiZhang (KPZ) equation converge to the KPZ fixed point, constructed earlier as a limit of the totally asymmetric simple exclusion process through exact formulas. Consequently, based on recent results of Wu [Tightness and local fluctuation

Rigidity properties of the cotangent complex J. Am. Math. Soc. (IF 3.5) Pub Date : 20220222
Benjamin Briggs,Srikanth IyengarThis work concerns a map φ : R → S \varphi \colon R\to S of commutative noetherian rings, locally of finite flat dimension. It is proved that the AndréQuillen homology functors are rigid, namely, if D n ( S / R ; − ) = 0 \mathrm {D}_n(S/R;)=0 for some n ≥ 1 n\ge 1 , then D i ( S / R ; − ) = 0 \mathrm {D}_i(S/R;)=0 for all i ≥ 2 i\ge 2 and φ {\varphi } is locally complete intersection. This extends

Integral models for spaces via the higher Frobenius J. Am. Math. Soc. (IF 3.5) Pub Date : 20220214
Allen YuanWe give a fully faithful integral model for simply connected finite complexes in terms of E ∞ \mathbb {E}_{\infty } ring spectra and the Nikolaus–Scholze Frobenius. The key technical input is the development of a homotopy coherent Frobenius action on a certain subcategory of p p complete E ∞ \mathbb {E}_{\infty } rings for each prime p p . Using this, we show that the data of a simply connected

On a conjecture of BravermanKazhdan J. Am. Math. Soc. (IF 3.5) Pub Date : 20211202
TsaoHsien ChenAbstract:In this article we prove a conjecture of BravermanKazhdan in [Geom. Funct. Anal. Special Volume (2000), pp. 237–278] on acyclicity of $\rho$Bessel sheaves on reductive groups. We do so by proving a vanishing conjecture proposed in our previous work [A vanishing conjecture: the GLn case, arXiv:1902.11190]. As a corollary, we obtain a geometric construction of the nonlinear Fourier kernel

Universal points in the asymptotic spectrum of tensors J. Am. Math. Soc. (IF 3.5) Pub Date : 20211123
Matthias Christandl,Péter Vrana,Jeroen ZuiddamMotivated by the problem of constructing fast matrix multiplication algorithms, Strassen (FOCS 1986, Crelle 1987–1991) introduced and developed the theory of asymptotic spectra of tensors. For any subsemiring X \mathcal {X} of tensors (under direct sum and tensor product), the duality theorem that is at the core of this theory characterizes basic asymptotic properties of the elements of X \mathcal

The Archimedean limit of random sorting networks J. Am. Math. Soc. (IF 3.5) Pub Date : 20211117
Duncan DauvergneAbstract:A sorting network (also known as a reduced decomposition of the reverse permutation) is a shortest path from $12 \cdots n$ to $n \cdots 21$ in the Cayley graph of the symmetric group $S_n$ generated by adjacent transpositions. We prove that in a uniform random $n$element sorting network $\sigma ^n$, all particle trajectories are close to sine curves with high probability. We also find the

The FontaineMazur conjecture in the residually reducible case J. Am. Math. Soc. (IF 3.5) Pub Date : 20211115
Lue PanAbstract:We prove new cases of FontaineMazur conjecture on twodimensional Galois representations over $\mathbb {Q}$ when the residual representation is reducible. Our approach is via a semisimple localglobal compatibility of the completed cohomology and a TaylorWiles patching argument for the completed homology in this case. As a key input, we generalize the work of SkinnerWiles in the ordinary

Hitchin fibrations, abelian surfaces, and the P=W conjecture J. Am. Math. Soc. (IF 3.5) Pub Date : 20211102
Mark de Cataldo, Davesh Maulik, Junliang ShenAbstract:We study the topology of Hitchin fibrations via abelian surfaces. We establish the P=W conjecture for genus $2$ curves and arbitrary rank. In higher genus and arbitrary rank, we prove that P=W holds for the subalgebra of cohomology generated by even tautological classes. Furthermore, we show that all tautological generators lie in the correct pieces of the perverse filtration as predicted

The SeibergWitten equations and the length spectrum of hyperbolic threemanifolds J. Am. Math. Soc. (IF 3.5) Pub Date : 20210802
Francesco Lin, Michael LipnowskiAbstract:We exhibit the first examples of hyperbolic threemanifolds for which the SeibergWitten equations do not admit any irreducible solution. Our approach relies on hyperbolic geometry in an essential way; it combines an explicit upper bound for the first eigenvalue on coexact $1$forms $\lambda _1^*$ on rational homology spheres which admit irreducible solutions together with a version of the

The meanfield limit of quantum Bose gases at positive temperature J. Am. Math. Soc. (IF 3.5) Pub Date : 20211008
Jürg Fröhlich, Antti Knowles, Benjamin Schlein, Vedran SohingerAbstract:We prove that the grand canonical Gibbs state of an interacting quantum Bose gas converges to the Gibbs measure of a nonlinear Schrödinger equation in the meanfield limit, where the density of the gas becomes large and the interaction strength is proportional to the inverse density. Our results hold in dimensions $d \leqslant 3$. For $d > 1$ the Gibbs measure is supported on distributions

Intersection complexes and unramified 𝐿factors J. Am. Math. Soc. (IF 3.5) Pub Date : 20211005
Yiannis Sakellaridis, Jonathan WangAbstract:Let $X$ be an affine spherical variety, possibly singular, and $\mathsf L^+X$ its arc space. The intersection complex of $\mathsf L^+X$, or rather of its finitedimensional formal models, is conjectured to be related to special values of local unramified $L$functions. Such relationships were previously established in Braverman–Finkelberg–Gaitsgory–Mirković for the affine closure of the quotient

Regularity theorem for totally nonnegative flag varieties J. Am. Math. Soc. (IF 3.5) Pub Date : 20210924
Pavel Galashin, Steven Karp, Thomas LamAbstract:We show that the totally nonnegative part of a partial flag variety $G/P$ (in the sense of Lusztig) is a regular CW complex, confirming a conjecture of Williams. In particular, the closure of each positroid cell inside the totally nonnegative Grassmannian is homeomorphic to a ball, confirming a conjecture of Postnikov.

Kudla–Rapoport cycles and derivatives of local densities J. Am. Math. Soc. (IF 3.5) Pub Date : 20210910
Chao Li, Wei ZhangAbstract:We prove the local Kudla–Rapoport conjecture, which is a precise identity between the arithmetic intersection numbers of special cycles on unitary Rapoport–Zink spaces and the derivatives of local representation densities of hermitian forms. As a first application, we prove the global Kudla–Rapoport conjecture, which relates the arithmetic intersection numbers of special cycles on unitary

Global regularity estimates for the Boltzmann equation without cutoff J. Am. Math. Soc. (IF 3.5) Pub Date : 20210910
Cyril Imbert, Luis SilvestreAbstract:We derive $C^\infty$ a priori estimates for solutions of the inhomogeneous Boltzmann equation without cutoff, conditional to pointwise bounds on their mass, energy and entropy densities. We also establish decay estimates for large velocities, for all derivatives of the solution.

On the tensor semigroup of affine KacMoody lie algebras J. Am. Math. Soc. (IF 3.5) Pub Date : 20210909
Nicolas RessayreAbstract:The support of the tensor product decomposition of integrable irreducible highest weight representations of a symmetrizable KacMoody Lie algebra $\mathfrak {g}$ defines a semigroup of triples of weights. Namely, given $\lambda$ in the set $P_+$ of dominant integral weights, $V(\lambda )$ denotes the irreducible representation of $\mathfrak {g}$ with highest weight $\lambda$. We are interested

Discrete logarithms in quasipolynomial time in finite fields of fixed characteristic J. Am. Math. Soc. (IF 3.5) Pub Date : 20210908
Thorsten Kleinjung, Benjamin WesolowskiAbstract:We prove that the discrete logarithm problem can be solved in quasipolynomial expected time in the multiplicative group of finite fields of fixed characteristic. More generally, we prove that it can be solved in the field of cardinality $p^n$ in expected time $(pn)^{2\log _2(n) + O(1)}$.

Effective randomness for continuous measures J. Am. Math. Soc. (IF 3.5) Pub Date : 20210830
Jan Reimann, Theodore SlamanAbstract:We investigate which infinite binary sequences (reals) are effectively random with respect to some continuous (i.e., nonatomic) probability measure. We prove that for every $n$, all but countably many reals are $n$random for such a measure, where $n$ indicates the arithmetical complexity of the MartinLöf tests allowed. The proof rests upon an application of Borel determinacy. Therefore

Control of eigenfunctions on surfaces of variable curvature J. Am. Math. Soc. (IF 3.5) Pub Date : 20210816
Semyon Dyatlov, Long Jin, Stéphane NonnenmacherAbstract:We prove a microlocal lower bound on the mass of high energy eigenfunctions of the Laplacian on compact surfaces of negative curvature, and more generally on surfaces with Anosov geodesic flows. This implies controllability for the Schrödinger equation by any nonempty open set, and shows that every semiclassical measure has full support. We also prove exponential energy decay for solutions

New bounds on the density of lattice coverings J. Am. Math. Soc. (IF 3.5) Pub Date : 20210728
Or Ordentlich, Oded Regev, Barak WeissAbstract:We obtain new upper bounds on the minimal density $\Theta _{n, \mathcal {K}}$ of lattice coverings of ${\mathbb {R}}^n$ by dilates of a convex body $\mathcal {K}$. We also obtain bounds on the probability (with respect to the natural HaarSiegel measure on the space of lattices) that a randomly chosen lattice $L$ satisfies $L+\mathcal {K}= {\mathbb {R}}^n$. As a step in the proof, we utilize

The conformal group of a compact simply connected Lorentzian manifold J. Am. Math. Soc. (IF 3.5) Pub Date : 20210712
Karin Melnick, Vincent PecastaingAbstract:We prove that the conformal group of a closed, simply connected, real analytic Lorentzian manifold is compact. D’Ambra proved in 1988 that the isometry group of such a manifold is compact [Invent. Math. 92 (1988), pp. 555–565]. Our result implies the Lorentzian Lichnerowicz Conjecture for real analytic Lorentzian manifolds with finite fundamental group.

Nilpotent structures and collapsing Ricciflat metrics on the K3 surface J. Am. Math. Soc. (IF 3.5) Pub Date : 20210625
HansJoachim Hein, Song Sun, Jeff Viaclovsky, Ruobing ZhangAbstract:We exhibit families of Ricciflat Kähler metrics on the K3 surface which collapse to an interval, with TianYau and TaubNUT metrics occurring as bubbles. There is a corresponding continuous surjective map from the $K3$ surface to the interval, with regular fibers diffeomorphic to either $3$tori or Heisenberg nilmanifolds.

Quasimorphisms on surface diffeomorphism groups J. Am. Math. Soc. (IF 3.5) Pub Date : 20210624
Jonathan Bowden, Sebastian Hensel, Richard WebbAbstract:We show that the identity component of the group of diffeomorphisms of a closed oriented surface of positive genus admits many unbounded quasimorphisms. As a corollary, we also deduce that this group is not uniformly perfect and its fragmentation norm is unbounded, answering a question of Burago–Ivanov–Polterovich. As a key tool we construct a hyperbolic graph on which these groups act, which

On the constant scalar curvature Kähler metrics (II)—Existence results J. Am. Math. Soc. (IF 3.5) Pub Date : 20210607
Xiuxiong Chen, Jingrui ChengAbstract:In this paper, we apply our previous estimates in Chen and Cheng [On the constant scalar curvature Kähler metrics (I): a priori estimates, Preprint] to study the existence of cscK metrics on compact Kähler manifolds. First we prove that the properness of $K$energy in terms of $L^1$ geodesic distance $d_1$ in the space of Kähler potentials implies the existence of cscK metrics. We also show

On the constant scalar curvature Kähler metrics (I)—A priori estimates J. Am. Math. Soc. (IF 3.5) Pub Date : 20210607
Xiuxiong Chen, Jingrui ChengAbstract:In this paper, we derive apriori estimates for constant scalar curvature Kähler metrics on a compact Kähler manifold. We show that higher order derivatives can be estimated in terms of a $C^0$ bound for the Kähler potential.

Homological mirror symmetry without correction J. Am. Math. Soc. (IF 3.5) Pub Date : 20210524
Mohammed AbouzaidAbstract:Let $X$ be a closed symplectic manifold equipped with a Lagrangian torus fibration over a base $Q$. A construction first considered by Kontsevich and Soibelman produces from this data a rigid analytic space $Y$, which can be considered as a variant of the $T$dual introduced by Strominger, Yau, and Zaslow. We prove that the Fukaya category of tautologically unobstructed graded Lagrangians

Geometric stochastic heat equations J. Am. Math. Soc. (IF 3.5) Pub Date : 20210430
Y. Bruned, F. Gabriel, M. Hairer, L. ZambottiAbstract:We consider a natural class of ${\mathbf {R}}^d$valued onedimensional stochastic partial differential equations (PDEs) driven by spacetime white noise that is formally invariant under the action of the diffeomorphism group on ${\mathbf {R}}^d$. This class contains in particular the KardarParisiZhang (KPZ) equation, the multiplicative stochastic heat equation, the additive stochastic heat

On the unicity of the theory of higher categories J. Am. Math. Soc. (IF 3.5) Pub Date : 20210420
Clark Barwick, Christopher SchommerPriesAbstract:We axiomatise the theory of $(\infty ,n)$categories. We prove that the space of theories of $(\infty ,n)$categories is a $B(\mathbb {Z}/2)^n$. We prove that Rezk’s complete Segal $\Theta _n$ spaces, Simpson and Tamsamani’s Segal $n$categories, the first author’s $n$fold complete Segal spaces, Kan and the first author’s $n$relative categories, and complete Segal space objects in any model

On the Ramanujan conjecture for automorphic forms over function fields I. Geometry J. Am. Math. Soc. (IF 3.5) Pub Date : 20210416
Will Sawin, Nicolas TemplierAbstract:Let $G$ be a split semisimple group over a function field. We prove the temperedness at unramified places of automorphic representations of $G$, subject to a local assumption at one place, stronger than supercuspidality, and assuming the existence of cyclic base change with good properties. Our method relies on the geometry of $\operatorname {Bun}_G$. It is independent of the work of Lafforgue

Algebraicity of the metric tangent cones and equivariant Kstability J. Am. Math. Soc. (IF 3.5) Pub Date : 20210409
Chi Li, Xiaowei Wang, Chenyang XuAbstract:We prove two new results on the $K$polystability of $\mathbb {Q}$Fano varieties based on purely algebrogeometric arguments. The first one says that any $K$semistable log Fano cone has a special degeneration to a uniquely determined $K$polystable log Fano cone. As a corollary, we combine it with the differentialgeometric results to complete the proof of DonaldsonSun’s conjecture which

A variational approach to the Yau–Tian–Donaldson conjecture J. Am. Math. Soc. (IF 3.5) Pub Date : 20210401
Robert Berman, Sébastien Boucksom, Mattias JonssonAbstract:We give a variational proof of a version of the Yau–Tian–Donaldson conjecture for twisted Kähler–Einstein currents, and use this to express the greatest (twisted) Ricci lower bound in terms of a purely algebrogeometric stability threshold. Our approach does not involve a continuity method or the Cheeger–Colding–Tian theory, and uses instead pluripotential theory and valuations. Along the

Plancherel theory for real spherical spaces: Construction of the Bernstein morphisms J. Am. Math. Soc. (IF 3.5) Pub Date : 20210325
Patrick Delorme, Friedrich Knop, Bernhard Krötz, Henrik SchlichtkrullAbstract:This paper lays the foundation for Plancherel theory on real spherical spaces $Z=G/H$, namely it provides the decomposition of $L^2(Z)$ into different series of representations via Bernstein morphisms. These series are parametrized by subsets of spherical roots which determine the fine geometry of $Z$ at infinity. In particular, we obtain a generalization of the MaassSelberg relations. As

Lebesgue spectrum of countable multiplicity for conservative flows on the torus J. Am. Math. Soc. (IF 3.5) Pub Date : 20210325
Bassam Fayad, Giovanni Forni, Adam KanigowskiAbstract:We study the spectral measures of conservative mixing flows on the $2$torus having one degenerate singularity. We show that, for a sufficiently strong singularity, the spectrum of these flows is typically Lebesgue with infinite multiplicity. For this, we use two main ingredients: (1) a proof of absolute continuity of the maximal spectral type for this class of nonuniformly stretching flows

Tropical curves, graph complexes, and top weight cohomology of ℳ_{ℊ} J. Am. Math. Soc. (IF 3.5) Pub Date : 20210202
Melody Chan, Søren Galatius, Sam PayneAbstract:We study the topology of a space parametrizing stable tropical curves of genus with volume , showing that its reduced rational homology is canonically identified with both the top weight cohomology of and also with the genus part of the homology of Kontsevich's graph complex. Using a theorem of Willwacher relating this graph complex to the GrothendieckTeichmüller Lie algebra, we deduce that

$K$theory and topological cyclic homology of Henselian pairs J. Am. Math. Soc. (IF 3.5) Pub Date : 20210127
Dustin Clausen, Akhil Mathew, Matthew MorrowGiven a henselian pair $(R, I)$ of commutative rings, we show that the relative $K$theory and relative topological cyclic homology with finite coefficients are identified via the cyclotomic trace $K \to \mathrm{TC}$. This yields a generalization of the classical GabberGilletThomasonSuslin rigidity theorem (for mod $n$ coefficients, with $n$ invertible in $R$) and McCarthy's theorem on relative

Extending holomorphic forms from the regular locus of a complex space to a resolution of singularities J. Am. Math. Soc. (IF 3.5) Pub Date : 20210126
Stefan Kebekus, Christian SchnellWe investigate under what conditions holomorphic forms defined on the regular locus of a reduced complex space extend to holomorphic (or logarithmic) forms on a resolution of singularities. We give a simple necessary and sufficient condition for this, whose proof relies on the Decomposition Theorem and Saito's theory of mixed Hodge modules. We use it to generalize the theorem of GrebKebekusKov\'acsPeternell

Hypertranscendence and linear difference equations J. Am. Math. Soc. (IF 3.5) Pub Date : 20210120
Boris Adamczewski, Thomas Dreyfus, Charlotte HardouinAfter H\"older proved his classical theorem about the Gamma function, there has been a whole bunch of results showing that solutions to linear difference equations tend to be hypertranscendental i.e. they cannot be solution to an algebraic differential equation). In this paper, we obtain the first complete results for solutions to general linear difference equations associated with the shift operator

Elliptic stable envelopes J. Am. Math. Soc. (IF 3.5) Pub Date : 20201209
Mina Aganagic, Andrei OkounkovWe construct stable envelopes in equivariant elliptic cohomology of Nakajima quiver varieties. In particular, this gives an elliptic generalization of the results of arXiv:1211.1287. We apply them to the computation of the monodromy of $q$difference equations arising the enumerative Ktheory of rational curves in Nakajima varieties, including the quantum KnizhnikZamolodchikov equations.

A sequence of polynomials with optimal condition number J. Am. Math. Soc. (IF 3.5) Pub Date : 20201208
Carlos Beltrán, Ujué Etayo, Jordi Marzo, Joaquim OrtegaCerdàWe find an explicit sequence of univariate polynomials of arbitrary degree with optimal condition number. This solves a problem posed by Michael Shub and Stephen Smale in 1993.

The test function conjecture for parahoric local models J. Am. Math. Soc. (IF 3.5) Pub Date : 20201207
Thomas J. Haines, Timo RicharzWe prove the test function conjecture of Kottwitz and the first named author for local models of Shimura varieties with parahoric level structure, and their analogues in equal characteristic.

Framed motives of algebraic varieties (after V. Voevodsky) J. Am. Math. Soc. (IF 3.5) Pub Date : 20201203
Grigory Garkusha, Ivan PaninUsing the machinery of framed sheaves developed by Voevodsky, a triangulated category of framed motives $SH_{S^1}^{fr}(k)$ is introduced and studied. To any smooth algebraic variety $X\in Sm/k$, the framed motive $M_{fr}(X)$ is associated in the category $SH_{S^1}^{fr}(k)$. Also, for any smooth scheme $X\in Sm/k$ an explicit quasifibrant motivic replacement of its suspension P^1spectrum is given

Nonconcentration of the chromatic number of a random graph J. Am. Math. Soc. (IF 3.5) Pub Date : 20201203
Annika HeckelWe show that the chromatic number of $G_{n, \frac 12}$ is not concentrated on fewer than $n^{\frac 14  \varepsilon}$ consecutive values. This addresses a longstanding question raised by Erdős and several other authors.

Characteristic cycles and the conductor of direct image J. Am. Math. Soc. (IF 3.5) Pub Date : 20201202
Takeshi SaitoWe prove the functoriality for proper pushforward of the characteristic cycles of constructible complexes by morphisms of smooth projective schemes over a perfect field, under the assumption that the direct image of the singular support has the dimension at most that of the target of the morphism. The functoriality is deduced from a conductor formula which is a special case for morphisms to curves

Cartier modules and cyclotomic spectra J. Am. Math. Soc. (IF 3.5) Pub Date : 20201202
Benjamin Antieau, Thomas NikolausWe construct and study a tstructure on ptypical cyclotomic spectra and explain how to recover crystalline cohomology of smooth schemes over perfect fields using this tstructure. Our main tool is a new approach to ptypical cyclotomic spectra via objects we call ptypical topological Cartier modules. Using these, we prove that the heart of the cyclotomic tstructure is the full subcategory of derived

The isoperimetric inequality for a minimal submanifold in Euclidean space J. Am. Math. Soc. (IF 3.5) Pub Date : 20201017
Simon BrendleWe prove an isoperimetric inequality which holds for minimal submanifolds in Euclidean space of arbitrary dimension and codimension. Our estimate is sharp if the codimension is at most $2$.

Large genus asymptotics for volumes of strata of abelian differentials J. Am. Math. Soc. (IF 3.5) Pub Date : 20200928
Amol AggarwalIn this paper we consider the large genus asymptotics for MasurVeech volumes of arbitrary strata of Abelian differentials. Through a combinatorial analysis of an algorithm proposed in 2002 by EskinOkounkov to exactly evaluate these quantities, we show that the volume $\nu_1 \big( \mathcal{H}_1 (m) \big)$ of a stratum indexed by a partition $m = (m_1, m_2, \ldots , m_n)$ is $\big( 4 + o(1) \big) \prod_{i

Billiards, quadrilaterals and moduli spaces J. Am. Math. Soc. (IF 3.5) Pub Date : 20200925
Alex Eskin,Curtis McMullen,Ronen Mukamel,Alex Wright 
Nonuniqueness and meanfield criticality for percolation on nonunimodular transitive graphs J. Am. Math. Soc. (IF 3.5) Pub Date : 20200923
Tom HutchcroftWe study Bernoulli bond percolation on nonunimodular quasitransitive graphs, and more generally graphs whose automorphism group has a nonunimodular quasitransitive subgroup. We prove that percolation on any such graph has a nonempty phase in which there are infinite light clusters, which implies the existence of a nonempty phase in which there are infinitely many infinite clusters. That is, we

Tame topology of arithmetic quotients and algebraicity of Hodge loci J. Am. Math. Soc. (IF 3.5) Pub Date : 20200915
B. Bakker, B. Klingler, J. TsimermanWe prove that the uniformizing map of any arithmetic quotient, as well as the period map associated to any pure polarized $\mathbb{Z}$variation of Hodge structure $\mathbb{V}$ on a smooth complex quasiprojective variety $S$, are topologically tame. As an easy corollary of these results and of PeterzilStarchenko's ominimal GAGA theorem we obtain that the Hodge locus of $(S, \mathbb{V})$ is a countable

Examples of compact Einstein fourmanifolds with negative curvature J. Am. Math. Soc. (IF 3.5) Pub Date : 20200914
Joel Fine, Bruno PremoselliWe give new examples of compact, negatively curved Einstein manifolds of dimension $4$. These are seemingly the first such examples which are not locally homogeneous. Our metrics are carried by a sequence of 4manifolds $(X_k)$ previously considered by Gromov and Thurston. The construction begins with a certain sequence $(M_k)$ of hyperbolic 4manifolds, each containing a totally geodesic surface $\Sigma_k$

Categorical joins J. Am. Math. Soc. (IF 3.5) Pub Date : 20200910
Alexander Kuznetsov, Alexander PerryWe introduce the notion of a categorical join, which can be thought of as a categorification of the classical join of two projective varieties. This notion is in the spirit of homological projective duality, which categorifies classical projective duality. Our main theorem says that the homological projective dual category of the categorical join is naturally equivalent to the categorical join of the

Bounds on 2torsion in class groups of number fields and integral points on elliptic curves J. Am. Math. Soc. (IF 3.5) Pub Date : 20200828
M. Bhargava, A. Shankar, T. Taniguchi, F. Thorne, J. Tsimerman, Y. ZhaoWe prove the first known nontrivial bounds on the sizes of the 2torsion subgroups of the class groups of cubic and higher degree number fields $K$ (the trivial bound being $O_{\epsilon}({\rm Disc}(K)^{1/2+\epsilon})$ by BrauerSiegel). This yields corresponding improvements to: 1) bounds of Brumer and Kramer on the sizes of 2Selmer groups and ranks of elliptic curves; 2) bounds of Helfgott and

Virtual homological spectral radii for automorphisms of surfaces J. Am. Math. Soc. (IF 3.5) Pub Date : 20200819
Yi LiuIn this paper, it is shown that any surface automorphism of positive mappingclass entropy possesses a virtual homological eigenvalue which lies outside the unit circle of the complex plane.

Pacman renormalization and selfsimilarity of the Mandelbrot set near Siegel parameters J. Am. Math. Soc. (IF 3.5) Pub Date : 20200616
Dzmitry Dudko, Mikhail Lyubich, Nikita SelingerIn the 1980s Branner and Douady discovered a surgery relating various limbs of the Mandelbrot set. We put this surgery in the framework of "Pacman Renormalization Theory" that combines features of quadraticlike and Siegel renormalizations. We show that Siegel renormalization periodic points (constructed by McMullen in the 1990s) can be promoted to pacman renormalization periodic points. Then we prove

Geometric stabilisation via $p$adic integration J. Am. Math. Soc. (IF 3.5) Pub Date : 20200615
Michael Groechenig, Dimitri Wyss, Paul ZieglerIn this article we give a new proof of Ng\^o's Geometric Stabilisation Theorem, which implies the Fundamental Lemma. This is a statement which relates the cohomology of Hitchin fibres for a quasisplit reductive group scheme $G$ to the cohomology of Hitchin fibres for the endoscopy groups $H_{\kappa}$. Our proof avoids the Decomposition and Support Theorem, instead the argument is based on results