Journal of the American Mathematical Society最新文献

{"title":"Billiards, quadrilaterals and moduli spaces","authors":"A. Eskin, C. McMullen, R. E. Mukamel, A. Wright","doi":"10.1090/jams/950","DOIUrl":"https://doi.org/10.1090/jams/950","url":null,"abstract":"Totally geodesic subvarieties. Let Mg denote the moduli space of Riemann surfaces X of genus g. If we also record n unordered marked points on X, we obtain the moduli space Mg,n. A subvariety V of moduli space is totally geodesic if it contains every Teichmüller geodesic that is tangent to it. It is primitive if it does not arise from a lower– dimensional moduli space via a covering construction. The first family of primitive, totally geodesic varieties of dimension one in Mg was discovered by Veech in the 1980s [V2]. These rare and remarkable Teichmüller curves are related to Jacobians with real multiplication and polygonal billiard tables with optimal dynamical properties. A second family was discovered shortly thereafter [Wa]. To date only a handful of families of Teichmüller curves are known. The first known primitive, totally geodesic variety of dimension larger than one is the recently discovered flex surface F ⊂ M1,3 [MMW]. The surface F is closely related to a new type of SL2(R)–invariant subvariety ΩG in the moduli space of","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":"1 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2020-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/jams/950","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43211750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dimensions of modular irreducible representations of semisimple Lie algebras","authors":"R. Bezrukavnikov, I. Losev","doi":"10.1090/jams/1017","DOIUrl":"https://doi.org/10.1090/jams/1017","url":null,"abstract":"In this paper we classify and give Kazhdan-Lusztig type character formulas for equivariantly irreducible representations of Lie algebras of reductive algebraic groups over a field of large positive characteristic. The equivariance is with respect to a group whose connected component is a torus. Character computation is done in two steps. First, we treat the case of distinguished \u0000\u0000 \u0000 p\u0000 p\u0000 \u0000\u0000-characters: those that are not contained in a proper Levi. Here we essentially show that the category of equivariant modules we consider is a cell quotient of an affine parabolic category \u0000\u0000 \u0000 \u0000 O\u0000 \u0000 mathcal {O}\u0000 \u0000\u0000. For this, we prove an equivalence between two categorifications of a parabolically induced module over the affine Hecke algebra conjectured by the first named author. For the general nilpotent \u0000\u0000 \u0000 p\u0000 p\u0000 \u0000\u0000-character, we get character formulas by explicitly computing the duality operator on a suitable equivariant K-group.","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":3.9,"publicationDate":"2020-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48883015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Strongly anisotropic type II blow up at an isolated point","authors":"Charles Collot, F. Merle, Pierre Raphael","doi":"10.1090/jams/941","DOIUrl":"https://doi.org/10.1090/jams/941","url":null,"abstract":"We consider the energy supercritical \u0000\u0000 \u0000 \u0000 d\u0000 +\u0000 1\u0000 \u0000 d+1\u0000 \u0000\u0000-dimensional semi-linear heat equation \u0000\u0000 \u0000 \u0000 \u0000 ∂\u0000 t\u0000 \u0000 u\u0000 =\u0000 Δ\u0000 u\u0000 +\u0000 \u0000 u\u0000 \u0000 p\u0000 \u0000 \u0000 ,\u0000  \u0000  \u0000 x\u0000 ∈\u0000 \u0000 \u0000 R\u0000 \u0000 \u0000 d\u0000 +\u0000 1\u0000 \u0000 \u0000 ,\u0000  \u0000  \u0000 p\u0000 ≥\u0000 3\u0000 ,\u0000  \u0000 d\u0000 ≥\u0000 14.\u0000 \u0000 begin{equation*} partial _tu=Delta u+u^{p}, xin Bbb R^{d+1}, pgeq 3, dgeq 14. end{equation*}\u0000 \u0000\u0000\u0000 A fundamental open problem on this canonical nonlinear model is to understand the possible blow-up profiles appearing after renormalisation of a singularity. We exhibit in this paper a new scenario corresponding to the first example of a strongly anisotropic blow-up bubble: the solution displays a completely different behaviour depending on the considered direction in space. A fundamental step of the analysis is to solve the reconnection problem in order to produce finite energy solutions which is the heart of the matter. The corresponding anistropic mechanism is expected to be of fundamental importance in other settings in particular in fluid mechanics. The proof relies on a new functional framework for the construction and stabilisation of type II bubbles in the parabolic setting using energy estimates only, and allows us to exhibit new unexpected blow-up speeds.","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":"33 1","pages":"527-607"},"PeriodicalIF":3.9,"publicationDate":"2020-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/jams/941","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46658049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Emergence of wandering stable components","authors":"P. Berger, S'ebastien Biebler","doi":"10.1090/jams/1005","DOIUrl":"https://doi.org/10.1090/jams/1005","url":null,"abstract":"We prove the existence of a locally dense set of real polynomial automorphisms of \u0000\u0000 \u0000 \u0000 \u0000 C\u0000 \u0000 2\u0000 \u0000 mathbb C^2\u0000 \u0000\u0000 displaying a wandering Fatou component; in particular this solves the problem of their existence, reported by Bedford and Smillie in 1991. These Fatou components have non-empty real trace and their statistical behavior is historic with high emergence. The proof is based on a geometric model for parameter families of surface real mappings. At a dense set of parameters, we show that the dynamics of the model displays a historic, high emergent, stable domain. We show that this model can be embedded into families of Hénon maps of explicit degree and also in an open and dense set of \u0000\u0000 \u0000 5\u0000 5\u0000 \u0000\u0000-parameter \u0000\u0000 \u0000 \u0000 C\u0000 r\u0000 \u0000 C^r\u0000 \u0000\u0000-families of surface diffeomorphisms in the Newhouse domain, for every \u0000\u0000 \u0000 \u0000 2\u0000 ≤\u0000 r\u0000 ≤\u0000 ∞\u0000 \u0000 2le rle infty\u0000 \u0000\u0000 and \u0000\u0000 \u0000 \u0000 r\u0000 =\u0000 ω\u0000 \u0000 r=omega\u0000 \u0000\u0000. This implies a complement of the work of Kiriki and Soma [Adv. Math. 306 (2017), pp. 524–588], a proof of the last Taken’s problem in the \u0000\u0000 \u0000 \u0000 C\u0000 \u0000 ∞\u0000 \u0000 \u0000 C^{infty }\u0000 \u0000\u0000 and \u0000\u0000 \u0000 \u0000 C\u0000 ω\u0000 \u0000 C^omega\u0000 \u0000\u0000-case. The main difficulty is that here perturbations are done only along finite-dimensional parameter families. The proof is based on the multi-renormalization introduced by Berger [Zoology in the Hénon family: twin babies and Milnor’s swallows, 2018].","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":3.9,"publicationDate":"2020-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47573275","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The conformal group of a compact simply connected Lorentzian manifold","authors":"K. Melnick, V. Pecastaing","doi":"10.1090/JAMS/976","DOIUrl":"https://doi.org/10.1090/JAMS/976","url":null,"abstract":"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. Our result implies the Lorentzian Lichnerowicz Conjecture for real analytic Lorentzian manifolds with finite fundamental group. \u0000Second version adds some clarifications and corrections.","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":3.9,"publicationDate":"2019-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48150865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hypertranscendence and linear difference equations","authors":"B. Adamczewski, T. Dreyfus, C. Hardouin","doi":"10.1090/jams/960","DOIUrl":"https://doi.org/10.1090/jams/960","url":null,"abstract":"<p>After Hölder 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 (<italic>i.e.</italic>, 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 <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"x right-arrow from bar x plus h\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>x</mml:mi>\u0000 <mml:mo stretchy=\"false\">↦<!-- ↦ --></mml:mo>\u0000 <mml:mi>x</mml:mi>\u0000 <mml:mo>+</mml:mo>\u0000 <mml:mi>h</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">xmapsto x+h</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> (<inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"h element-of double-struck upper C Superscript asterisk\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>h</mml:mi>\u0000 <mml:mo>∈<!-- ∈ --></mml:mo>\u0000 <mml:msup>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">C</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mo>∗<!-- ∗ --></mml:mo>\u0000 </mml:msup>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">hin mathbb {C}^*</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>), the <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"q\">\u0000 <mml:semantics>\u0000 <mml:mi>q</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">q</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-difference operator <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"x right-arrow from bar q x\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>x</mml:mi>\u0000 <mml:mo stretchy=\"false\">↦<!-- ↦ --></mml:mo>\u0000 <mml:mi>q</mml:mi>\u0000 <mml:mi>x</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">xmapsto qx</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> (<inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"q element-of double-struck upper C Superscript asterisk\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>q</mml:mi>\u0000 <mml:mo>∈<!-- ∈ --></mml:mo>\u0000 <mml:msup>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">C</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mo>∗<!-- ∗ --></mml:mo>\u0000 </mml:msup>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">qin mathbb {C}^*</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> not a root of unity), and the Mahler operator <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"x rig","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":3.9,"publicationDate":"2019-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44873591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global regularity estimates for the Boltzmann equation without cut-off","authors":"C. Imbert, L. Silvestre","doi":"10.1090/JAMS/986","DOIUrl":"https://doi.org/10.1090/JAMS/986","url":null,"abstract":"We derive $C^infty$ a priori estimates for solutions of the inhomogeneous Boltzmann equation without cut-off, conditional to point-wise bounds on their mass, energy and entropy densities. We also establish decay estimates for large velocities, for all derivatives of the solution.","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":3.9,"publicationDate":"2019-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46176378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quasi-morphisms on surface diffeomorphism groups","authors":"Jonathan Bowden, S. Hensel, Richard C. H. Webb","doi":"10.1090/JAMS/981","DOIUrl":"https://doi.org/10.1090/JAMS/981","url":null,"abstract":"We show that the identity component of the group of diffeomorphisms of a closed oriented surface of positive genus admits many unbounded quasi-morphisms. 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. \u0000To do this, we introduce an analogue of the curve graph from the theory of mapping class groups. We show that it is hyperbolic and that the natural group action by isometries satisfies the criterion of Bestvina-Fujiwara.","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":3.9,"publicationDate":"2019-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43553009","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Control of eigenfunctions on surfaces of variable curvature","authors":"S. Dyatlov, Long Jin, S. Nonnenmacher","doi":"10.1090/jams/979","DOIUrl":"https://doi.org/10.1090/jams/979","url":null,"abstract":"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 to the damped wave equation on such surfaces, for any nontrivial damping coefficient. These results extend previous works (see Semyon Dyatlov and Long Jin [Acta Math. 220 (2018), pp. 297–339] and Long Jin [Comm. Math. Phys. 373 (2020), pp. 771–794]), which considered the setting of surfaces of constant negative curvature.\u0000\u0000The proofs use the strategy of Semyon Dyatlov and Long Jin [Acta Math. 220 (2018), pp. 297–339 and Long Jin [Comm. Math. Phys. 373 (2020), pp. 771–794] and rely on the fractal uncertainty principle of Jean Bourgain and Semyon Dyatlov [Ann. of Math. (2) 187 (2018), pp. 825–867]. However, in the variable curvature case the stable/unstable foliations are not smooth, so we can no longer associate to these foliations a pseudodifferential calculus of the type used by Semyon Dyatlov and Joshua Zahl [Geom. Funct. Anal. 26 (2016), pp. 1011–1094]. Instead, our argument uses Egorov’s theorem up to local Ehrenfest time and the hyperbolic parametrix of Stéphane Nonnenmacher and Maciej Zworski [Acta Math. 203 (2009), pp. 149–233], together with the \u0000\u0000 \u0000 \u0000 C\u0000 \u0000 1\u0000 +\u0000 \u0000 \u0000 C^{1+}\u0000 \u0000\u0000 regularity of the stable/unstable foliations.","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":3.9,"publicationDate":"2019-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43735354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Duality between the pseudoeffective and the movable cone on a projective manifold","authors":"David Witt Nyström","doi":"10.1090/JAMS/922","DOIUrl":"https://doi.org/10.1090/JAMS/922","url":null,"abstract":"","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":"32 1","pages":"675-689"},"PeriodicalIF":3.9,"publicationDate":"2019-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/JAMS/922","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42647432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}