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作者：Schwartz, R. I. C. H. A. R. D. EvAN
作者单位：Brown University
摘要：We prove that a smooth embedded paper Moebius band must have aspect ratio greater than \/3. We also prove that any sequence of smooth embedded paper Moebius bands whose aspect ratio converges to \/3 must converge, up to isometry, to the triangular Moebius band. These results answer the mimimum aspect ratio question discussed by W. Wunderlich in 1962 and prove the more specific conjecture of B. Halpern and C. Weaver from 1977.
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作者：Schwartz, R. I. C. H. A. R. D. EvAN
作者单位：Brown University
摘要：We prove that a smooth embedded paper Moebius band must have aspect ratio greater than \/3. We also prove that any sequence of smooth embedded paper Moebius bands whose aspect ratio converges to \/3 must converge, up to isometry, to the triangular Moebius band. These results answer the mimimum aspect ratio question discussed by W. Wunderlich in 1962 and prove the more specific conjecture of B. Halpern and C. Weaver from 1977.
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作者：Yang, Lei
作者单位：Institute for Advanced Study - USA; National University of Singapore
摘要：In this paper, we will prove an effective version of Ratner's equidistribution theorem for unipotent orbits in SL(3, R)/SL(3, Z) with a natural Diophantine condition.
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作者：Manolescu, Ciprian; Ozsvath, Peter s.; Thurston, Dylan p.
作者单位：Stanford University; Princeton University; Indiana University System; Indiana University Bloomington
摘要：We give combinatorial descriptions of the Heegaard Floer homology groups for arbitrary three-manifolds (with coefficients in Z/2Z). The descriptions are based on presenting the three-manifold as an integer surgery on a link in the three-sphere, and then using a grid diagram for the link. We also give combinatorial descriptions of the mod 2 Ozsv & aacute;th-Szab & oacute; mixed invariants of closed four-manifolds, also in terms of grid diagrams.
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作者：Poels, Anthony
作者单位：Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Jean Monnet; Universite Lyon 1; Ecole Centrale de Lyon; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：In his seminal 1961 paper, Wirsing studied how well a given transcendental real number xi can be approximated by algebraic numbers alpha of degree at most n for a given positive integer n , in terms of the so-called naive height H(alpha) of alpha . He showed that the supremum omega & lowast;n(xi) of all omega for which infinitely many such alpha have |xi- alpha| <= H(alpha)-omega-1 is at least (n + 1)/2. He also asked if we could even have omega & lowast;n(xi) >= nas it is generally expected. ...
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作者：Cohen, Alex
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We prove that if a fractal set in Rd avoids lines in a certain quantitative sense, which we call line porosity, then it has a fractal uncertainty principle. The main ingredient is a new higher-dimensional Beurling-Malliavin multiplier theorem.
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作者：Eberle, Simon; Figalli, Alessio; Weiss, Georg s.
作者单位：Basque Center for Applied Mathematics (BCAM); Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Duisburg Essen
摘要：The characterization of global solutions to the obstacle problems in RN, or equivalently of null quadrature domains, has been studied for more than 90 years. In this paper, we give a conclusive answer to this problem by proving the following long-standing conjecture: The coincidence set of a global solution to the obstacle problem is either a half-space, an ellipsoid, a paraboloid, or a cylinder with an ellipsoid or a paraboloid as base.
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作者：Betts, L. alexander; Stix, Jakob
作者单位：Cornell University; Goethe University Frankfurt
摘要：Let K be a number field not containing a CM subfield. For any smooth projective curve Y/K of genus >= 2, we prove that the image of the Selmer part of Grothendieck's section set inside the Kv-rational points Y (Kv) is finite for every finite place v. This gives an unconditional verification of a prediction of Grothendieck's section conjecture. In the process of proving our main result, we also refine and extend the method of Lawrence and Venkatesh, with potential consequences for explicit comp...
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作者：Bishop, Christopher J.
作者单位：State University of New York (SUNY) System; Stony Brook University
摘要：This paper gives geometric characterizations of the Weil-Petersson class of rectifiable quasicircles, i.e., the closure of the smooth planar curves in the Weil-Petersson metric on universal Teichmuller space defined by Takhtajan and Teo. Although motivated by the planar case, many of our characterizations make sense for curves in Rn and remain equivalent in all dimensions. We prove that Gamma is Weil-Petersson if and only if it is well approximated by polygons in a precise sense, has finite Mo...
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作者：Kings, Guido; Sprang, Johannes
作者单位：University of Regensburg; University of Duisburg Essen
摘要：We show that for an arbitrary totally complex number field L the (regularized) critical L-values of algebraic Hecke characters of L divided by certain periods are algebraic integers. This relies on a new construction of an equivariant coherent cohomology class with values in the completion of the Poincare bundle on an abelian scheme A. From this we obtain a cohomology class for the automorphism group of a CM abelian scheme A with values in some canonical bundles, which can be explicitly calcul...
