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作者：Blumenthal, Alex; Young, Lai-Sang
作者单位：New York University
摘要：We consider C-2 Frechet differentiable mappings of Banach spaces leaving invariant compactly supported Borel probability measures, and study the relation between entropy and volume growth for a natural notion of volume defined on finite dimensional subspaces. SRB measures are characterized as exactly those measures for which entropy is equal to volume growth on unstable manifolds, equivalently the sum of positive Lyapunov exponents of the map. In addition to numerous difficulties incurred by o...
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作者：Miao, Shuang; Yu, Pin
作者单位：University of Michigan System; University of Michigan; Tsinghua University
摘要：The paper is devoted to the study of shock formation of the 3-dimensional quasilinear wave equation -(1 + 3G ''(0)(partial derivative(t)phi)(2))partial derivative(2)(t)phi + Delta phi = 0, where is a non-zero constant. We will exhibit a family of smooth initial data and show that the foliation of the incoming characteristic hypersurfaces collapses. Similar to 1-dimensional conservational laws, we refer this specific type breakdown of smooth solutions as shock formation. Since satisfies the cla...
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作者：Baraud, Y.; Birge, L.; Sart, M.
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：The aim of this paper is to present a new estimation procedure that can be applied in various statistical frameworks including density and regression and which leads to both robust and optimal (or nearly optimal) estimators. In density estimation, they asymptotically coincide with the celebrated maximum likelihood estimators at least when the statistical model is regular enough and contains the true density to estimate. For very general models of densities, including non-compact ones, these es...
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作者：Saroch, Jan
作者单位：Charles University Prague
摘要：We show that, over any ring, a module C is the codomain of a right almost split map, if and only if C is finitely presented with a local endomorphism ring. Thus we answer a 40-year-old question by Maurice Auslander.
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作者：Oh, Hee; Winter, Dale
作者单位：Yale University; Korea Institute for Advanced Study (KIAS); Institute for Advanced Study - USA
摘要：For a hyperbolic rational map f of degree at least two on the Riemann sphere, we obtain estimates for the number of primitive periodic orbits of f ordered by their multiplier, and establish equidistribution of the associated holonomies, both with power saving error terms.
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作者：Gilmer, Patrick M.; Masbaum, Gregor
作者单位：Louisiana State University System; Louisiana State University; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite
摘要：For a prime, and an integer, we use Topological Quantum Field Theory (TQFT) to study a family of highest weight modules for the symplectic group where K is an algebraically closed field of characteristic p. This permits explicit formulae for the dimension and the formal character of for these highest weights.
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作者：Bhatt, Bhargav; Scholze, Peter
作者单位：University of Michigan System; University of Michigan; University of Bonn
摘要：We prove that the Witt vector affine Grassmannian, which parametrizes W(k)-lattices in for a perfect field k of characteristic p, is representable by an ind-(perfect scheme) over k. This improves on previous results of Zhu by constructing a natural ample line bundle. Along the way, we establish various foundational results on perfect schemes, notably h-descent results for vector bundles.
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作者：Saito, Takeshi
作者单位：University of Tokyo
摘要：We define the characteristic cycle of an ,tale sheaf as a cycle on the cotangent bundle of a smooth variety in positive characteristic using the singular support recently defined by Beilinson. We prove a formula A la Milnor for the total dimension of the space of vanishing cycles and an index formula computing the Euler-Poincar, characteristic, generalizing the Grothendieck-Ogg-Shafarevich formula to higher dimension. An essential ingredient of the construction and the proof is a partial gener...
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作者：McMullen, Curtis T.; Mohammadi, Amir; Oh, Hee
作者单位：Harvard University; University of California System; University of California San Diego; Yale University; Korea Institute for Advanced Study (KIAS)
摘要：This paper initiates the study of rigidity for immersed, totally geodesic planes in hyperbolic 3-manifolds M of infinite volume. In the case of an acylindrical 3-manifold whose convex core has totally geodesic boundary, we show that the closure of any immersed geodesic plane is a properly immersed submanifold of M. On the other hand, we show that rigidity fails for quasifuchsian manifolds.
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作者：Phong, Duong H.; Picard, Sebastien; Zhang, Xiangwen
作者单位：Columbia University; University of California System; University of California Irvine
摘要：The Fu-Yau equation is an equation introduced by Fu and Yau as a generalization to arbitrary dimensions of an ansatz for the Strominger system. As in the Strominger system, it depends on a slope parameter . The equation was solved in dimension 2 by Fu and Yau in two successive papers for , and for . In the present paper, we solve the Fu-Yau equation in arbitrary dimension for . To our knowledge, these are the first non-trivial solutions of the Fu-Yau equation in any dimension strictly greater ...
