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作者：Banks, Peter; Panzer, Erik; Pym, Brent
作者单位：University of Oxford; University of Edinburgh; McGill University
摘要：Kontsevich's 1997 formula for the deformation quantization of Poisson brackets is a Feynman expansion involving volume integrals over moduli spaces of marked disks. We develop a systematic theory of integration on these moduli spaces via suitable algebras of polylogarithms, and use it to prove that Kontsevich's integrals can be expressed as integer-linear combinations of multiple zeta values. Our proof gives a concrete algorithm for calculating the integrals, which we have used to produce the ...
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作者：Marrakchi, Amine
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：We show that a factor M is full if and only if the C*-algebra generated by its left and right regular representations contains the compact operators. We prove that the bicentralizer flow of a type III1 factor is always ergodic. As a consequence, for any type III1 factor M and any lambda is an element of]0, 1], there exists an irreducible AFD type III lambda subfactor with expectation in M. Moreover, any type III1 factor M which satisfies M congruent to M (circle times) over bar R-lambda for so...
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作者：Xi, Ping
作者单位：Xi'an Jiaotong University
摘要：By elaborating a two-dimensional Selberg sieve with asymptotics and equidistributions of Kloosterman sums from l\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell $$\end{document}-adic cohomology, as well as a Bombieri-Vinogradov type mean value theorem for Kloosterman sums in arithmetic progressions, it is prove...
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作者：Pierce, Lillian B.; Turnage-Butterbaugh, Caroline L.; Wood, Melanie Matchett
作者单位：Duke University; Institute for Advanced Study - USA; Carleton College; University of California System; University of California Berkeley
摘要：We prove a new effective Chebotarev density theorem for Galois extensions L/Q that allows one to count small primes (even as small as an arbitrarily small power of the discriminant of L); this theorem holds for the Galois closures of almost all number fields that lie in an appropriate family of field extensions. Previously, applying Chebotarev in such small ranges required assuming the Generalized Riemann Hypothesis. The error term in this new Chebotarev density theorem also avoids the effect ...
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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...
