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作者：Barany, Balazs; Hochman, Michael; Rapaport, Ariel
作者单位：MTA-BME Stochastics Research Group; Budapest University of Technology & Economics; Hebrew University of Jerusalem
摘要：Let X=?phi iX be a strongly separated self-affine set in R2 (or one satisfying the strong open set condition). Under mild non-conformality and irreducibility assumptions on the matrix parts of the phi i, we prove that dimX is equal to the affinity dimension, and similarly for self-affine measures and the Lyapunov dimension. The proof is via analysis of the dimension of the orthogonal projections of the measures, and relies on additive combinatorics methods.
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作者：Marques, Fernando C.; Neves, Andre; Song, Antoine
作者单位：Princeton University; University of Chicago; Imperial College London
摘要：For almost all Riemannian metrics (in the C-infinity Baire sense) on a closed manifold Mn+1, 3 <= (n + 1) <= 7, we prove that there is a sequence of closed, smooth, embedded, connected minimal hypersurfaces that is equidistributed in M. This gives a quantitative version of the main result of Irie et al. (Ann Math 187(3): 963-972, 2018), that established density of minimal hypersurfaces for generic metrics. As in Irie et al. (2018), the main tool is the Weyl Law for the Volume Spectrum proven b...
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作者：Bartels, Arthur; Bestvina, Mladen
作者单位：University of Munster; Utah System of Higher Education; University of Utah
摘要：We prove the Farrell-Jones Conjecture for mapping class groups. The proof uses the Masur-Minsky theory of the large scale geometry of mapping class groups and the geometry of the thick part of Teichmuller space. The proof is presented in an axiomatic setup, extending the projection axioms in Bestvina et al. (Publ Math Inst Hautes Etudes Sci 122:1-64, 2015). More specifically, we prove that the action of on the Thurston compactification of Teichmuller space is finitely F-amenable for the family...
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作者：Hyde, James; Lodha, Yash
作者单位：University of St Andrews; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We construct examples of finitely generated infinite simple groups of homeomorphisms of the real line. Equivalently, these are examples of finitely generated simple left (or right) orderable groups. This answers a well known open question of Rhemtulla from 1980 concerning the existence of such groups. In fact, our construction provides a family of continuum many isomorphism types of groups with these properties.
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作者：Maynard, James
作者单位：University of Oxford
摘要：Let a0{0,...,9}. We show there are infinitely many prime numbers which do not have the digit a0 in their decimal expansion. The proof is an application of the Hardy-Littlewood circle method to a binary problem, and rests on obtaining suitable Type I' and Type II' arithmetic information for use in Harman's sieve to control the minor arcs. This is obtained by decorrelating Diophantine conditions which dictate when the Fourier transform of the primes is large from digital conditions which dictate...
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作者：Ntalampekos, Dimitrios
作者单位：State University of New York (SUNY) System; Stony Brook University
摘要：We prove that the Sierpiski gasket is non-removable for quasiconformal maps, thus answering a question of Bishop (NSF Research Proposal, 2015. http://www.math.stonybrook.edu/similar to bishop/vita/nsf15.pdf). The proof involves a new technique of constructing an exceptional homeomorphism from R-2 into some non-planar surface S, and then embedding this surface quasisymmetrically back into the plane by using the celebrated Bonk-Kleiner Theorem (Bonk and Kleiner in Invent Math 150(1):127-183, 200...
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作者：Idrissi, Najib
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
摘要：We prove the validity over R of a commutative differential graded algebra model of configuration spaces for simply connected closed smooth manifolds, answering a conjecture of Lambrechts-Stanley. We get as a result that the real homotopy type of such configuration spaces only depends on the real homotopy type of the manifold. We moreover prove, if the dimension of the manifold is at least 4, that our model is compatible with the action of the Fulton-MacPherson operad (weakly equivalent to the ...
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作者：Goldstein, Michael; Schlag, Wilhelm; Voda, Mircea
作者单位：University of Toronto; Yale University; University of Chicago
摘要：We study multi-frequency quasiperiodic Schrodinger operators on Z. We prove that for a large real analytic potential satisfying certain restrictions the spectrum consists of a single interval. The result is a consequence of a criterion for the spectrum to contain an interval at a given location that we establish non-perturbatively in the regime of positive Lyapunov exponent.
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作者：Antieau, Benjamin; Auel, Asher; Ingalls, Colin; Krashen, Daniel; Lieblich, Max
作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Yale University; Rutgers University System; Rutgers University New Brunswick; Rutgers University Newark; University of Washington; University of Washington Seattle
摘要：The standard period-index conjecture for Brauer groups of p-adic surfaces S predicts that ind(alpha) vertical bar per(alpha)3 for every alpha is an element of Br(Q(p)(S)). Using Gabber's theory of prime-to-l alterations and the deformation theory of twisted sheaves, we prove that ind(alpha) vertical bar per(alpha) 4 for alpha of period prime to 6p, giving the first uniform period-index bounds over such fields.
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作者：Guo, Shaoming; Zhang, Ruixiang
作者单位：Institute for Advanced Study - USA; Indiana University System; Indiana University Bloomington; University of Wisconsin System; University of Wisconsin Madison
摘要：We prove a sharp upper bound on the number of integer solutions of the Parsell-Vinogradov system in every dimension d >= 2
