2017

最新文章

• Progression-free sets in Z4n are exponentially small AI翻译
  作者：Croot, Ernie; Lev, Vsevolod F.; Pach, Peter Pal
• The triviality of the 61-stem in the stable homotopy groups of spheres AI翻译
  作者：Wang, Guozhen; Xu, Zhouli
  摘要：We prove that the 2-primary pi(61) is zero. As a consequence, the Kervaire invariant element theta(5) is contained in the strictly defined 4-fold Toda bracket < 2, theta(4), theta(4) 2 >. Our result has a geometric corollary: the 61-sphere has a unique smooth structure, and it is the last odd dimensional case - the only ones are S-1, S-3, S-5 and S-61. Our proof is a computation of homotopy groups of spheres. A major part of this paper is to prove an Adams differential d(3)(D-3) = B-3. We prov...
• Dynamical spectral rigidity among Z2 -symmetric strictly convex domains close to a circle AI翻译
  作者：De Simoi, Jacopo; Kaloshin, Vadim; Wei, Qiaoling
  摘要：We show that any sufficiently (finitely) smooth Z(2) -symmetric strictly convex domain sufficiently close to a circle is dynamically spectrally rigid; i.e., all deformations among domains in the same class that preserve the length of all periodic orbits of the associated billiard flow must necessarily be isometric deformations. This gives a partial answer to a question of P. Sarnak.
• Monochromatic sums and products in N AI翻译
  作者：Moreira, Joel
  摘要：An old question in Ramsey theory asks whether any finite coloring of the natural numbers admits a monochromatic pair {x + y, xy}. We answer this question affirmatively in a strong sense by exhibiting a large new class of nonlinear patterns that can be found in a single cell of any finite partition of N. Our proof involves a correspondence principle that transfers the problem into the language of topological dynamics. As a corollary of our main theorem we obtain partition regularity for new typ...
• Derived categories and Deligne-Lusztig varieties II AI翻译
  作者：Bonnafe, Cedric; Dat, Jean-Francois; Rouquier, Raphael
  摘要：This paper is a continuation and a completion of the work of the first and the third author on the Jordan decomposition. We extend the Jordan decomposition of blocks: we show that blocks of finite groups of Lie type in nondescribing characteristic are Morita equivalent to blocks of subgroups associated to isolated elements of the dual group this is the modular version of a fundamental result of Lusztig, and the best approximation of the character -theoretic Jordan decomposition that can be obt...
• Measurable circle squaring AI翻译
  作者：Grabowski, Lukasz; Mathe, Andras; Pikhurko, Oleg
  摘要：Laczkovich proved that if bounded subsets A and B of R-k have the same nonzero Lebesgue measure and the upper box dimension of the boundary of each set is less than k, then there is a partition of A into finitely many parts that can be translated to form a partition of B. Here we show that it can be additionally required that each part is both Baire and Lebesgue measurable. As special cases, this gives measurable and translation-only versions of Tarski's circle squaring and Hilbert's third pro...
• Shtukas and the Taylor expansion of L-functions AI翻译
  作者：Yun, Zhiwei; Zhang, Wei
  摘要：We define the Heegner Drinfeld cycle on the moduli stack of Drinfeld Shtukas of rank two with r-modifications for an even integer r. We prove an identity between (1) the r-th central derivative of the quadratic base change L-function associated to an everywhere unramified cuspidal automorphic representation pi of PGL(2), and (2) the self-intersection number of the pi-isotypic component of the Heegner Drinfeld cycle. This identity can be viewed as a function-field analog of the Waldspurger and ...
• The Apollonian structure of integer superharmonic matrices AI翻译
  作者：Levine, Lionel; Pegden, Wesley; Smart, Charles K.
  摘要：We prove that the set of quadratic growths attainable by integer-valued superharmonic functions on the lattice Z(2) has the structure of an Apollonian circle packing. This completely characterizes the PDE that determines the continuum scaling limit of the Abelian sandpile on the lattice Z(2).
• The sphere packing problem in dimension 8The sphere packing problem in dimension 8 AI翻译
  作者：Viazovska, Maryna S.
  摘要：In this paper we prove that no packing of unit balls in Euclidean space R-8 has density greater than that of the E8-lattice packing.
• Coatings of the half-plane of Drinfeld and p-adique Langlands correspondence AI翻译
  作者：Dospinescu, Gabriel; Le Bras, Arthur-Cesar
  摘要：We describe the de Rham complex of the etale coverings of Drinfeld's p-adic upper half-plane for GL(2)(Q(p)). Conjectured by Breuil and Strauch, this description gives a geometric realization of the p-adic local Langlands correspondence for certain two-dimensional de Rham representations of Gal((Q(p)) over bar /Q(p)).