-
作者：Ford, Kevin; Wooley, Trevor D.
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; University of Bristol
摘要：We enhance the efficient congruencing method for estimating Vinogradov's integral for moments of order 2s, with . In this way, we prove the main conjecture for such even moments when , showing that the moments exhibit strongly diagonal behaviour in this range. There are improvements also for larger values of s, these finding application to the asymptotic formula in Waring's problem.
-
作者：Galatius, Soren; Randal-Williams, Oscar
作者单位：Stanford University; University of Cambridge
摘要：We prove an analogue of the Madsen-Weiss theorem for high-dimensional manifolds. In particular, we explicitly describe the ring of characteristic classes of smooth fibre bundles whose fibres are connected sums of g copies of S (n) xS (n) , in the limit . Rationally it is a polynomial ring in certain explicit generators, giving a high-dimensional analogue of Mumford's conjecture. More generally, we study a moduli space of those null-bordisms of a fixed (2n-1)-dimensional manifold P which are (n...
-
作者：Scott, Alexander D.; Sokal, Alan D.
作者单位：University of Oxford; New York University; University of London; University College London
摘要：We prove the complete monotonicity on for suitable inverse powers of the spanning-tree polynomials of graphs and, more generally, of the basis generating polynomials of certain classes of matroids. This generalizes a result of SzegA and answers, among other things, a long-standing question of Lewy and Askey concerning the positivity of Taylor coefficients for certain rational functions. Our proofs are based on two ab-initio methods for proving that is completely monotone on a convex cone C: th...
-
作者：Birbrair, Lev; Neumann, Walter D.; Pichon, Anne
作者单位：Universidade Federal do Ceara; Columbia University; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We describe a natural decomposition of a normal complex surface singularity (X, 0) into its thick and thin parts. The former is essentially metrically conical, while the latter shrinks rapidly in thickness as it approaches the origin. The thin part is empty if and only if the singularity is metrically conical; the link of the singularity is then Seifert fibered. In general the thin part will not be empty, in which case it always carries essential topology. Our decomposition has some analogy wi...
-
作者：Lieb, Elliott H.; Solovej, Jan Philip
作者单位：Princeton University; Princeton University; University of Copenhagen
摘要：Wehrl used Glauber coherent states to define a map from quantum density matrices to classical phase space densities and conjectured that for Glauber coherent states the mininimum classical entropy would occur for density matrices equal to projectors onto coherent states. This was proved by Lieb in 1978 who also extended the conjecture to Bloch SU(2) spin-coherent states for every angular momentum J. This conjecture is proved here. We also recall our 1991 extension of the Wehrl map to a quantum...
-
作者：Nazarov, Fedor; Tolsa, Xavier; Volberg, Alexander
作者单位：University System of Ohio; Kent State University; Kent State University Salem; Kent State University Kent; ICREA; Autonomous University of Barcelona; Michigan State University
摘要：We prove that if mu is a d-dimensional Ahlfors-David regular measure in , then the boundedness of the d-dimensional Riesz transform in L (2)(mu) implies that the non-BAUP David-Semmes cells form a Carleson family. Combined with earlier results of David and Semmes, this yields the uniform rectifiability of mu.
