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• Finitely generated infinite simple groups of homeomorphisms of the real line AI翻译
  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.
• Primes with restricted digits AI翻译
  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...
• The Lambrechts-Stanley model of configuration spaces AI翻译
  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 ...
• On integer solutions of Parsell-Vinogradov systems AI翻译
  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
• K-theoretic obstructions to bounded t-structures AI翻译
  作者：Antieau, Benjamin; Gepner, David; Heller, Jeremiah
  作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; University of Melbourne; University of Illinois System; University of Illinois Urbana-Champaign
  摘要：Schlichting conjectured that the negative K-groups of small abelian categories vanish and proved this for noetherian abelian categories and for all abelian categories in degree -1. The main results of this paper are that K-1(E) vanishes when E is a small stable -category with a bounded t-structure and that K-n(E) vanishes for all n1 when additionally the heart of E is noetherian. It follows that Barwick's theorem of the heart holds for nonconnective K-theory spectra when the heart is noetheria...
• Integral models of Hilbert modular varieties in the ramified case, deformations of modular Galois representations, and weight one forms AI翻译
  作者：Sasaki, Shu
  作者单位：University of Duisburg Essen
  摘要：We prove the strong Artin conjecture for continuous, totally odd, two-dimensional representations of the absolute Galois group of a totally real field F.
• W-algebras as coset vertex algebras AI翻译
  作者：Arakawa, Tomoyuki; Creutzig, Thomas; Linshaw, Andrew R.
  作者单位：Kyoto University; University of Alberta; University of Denver
  摘要：We prove the long-standing conjecture on the coset construction of the minimal series principal W-algebras of ADE types in full generality. We do this by first establishing Feigin's conjecture on the coset realization of the universal principal W-algebras, which are not necessarily simple. As consequences, the unitarity of the discrete series of principal W-algebras is established, a second coset realization of rational and unitary W-algebras of type A and D are given and the rationality of Ka...
• Tropical refined curve counting from higher genera and lambda classes AI翻译
  作者：Bousseau, Pierrick
  作者单位：Imperial College London
  摘要：Block and Gottsche have defined a q-number refinement of counts of tropical curves in R2. Under the change of variables q=eiu, we show that the result is a generating series of higher genus log Gromov-Witten invariants with insertion of a lambda class. This gives a geometric interpretation of the Block-Gottsche invariants and makes their deformation invariance manifest.
• Deciding isomorphy using Dehn fillings, the splitting case AI翻译
  作者：Dahmani, Francois; Touikan, Nicholas
  作者单位：Centre National de la Recherche Scientifique (CNRS); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); University of New Brunswick
  摘要：We solve Dehn's isomorphism problem for virtually torsion-free relatively hyperbolic groups with nilpotent parabolic subgroups. We do so by reducing the isomorphism problem to three algorithmic problems in the parabolic subgroups, namely the isomorphism problem, separation of torsion (in their outer automorphism groups) by congruences, and the mixed Whitehead problem, an automorphism group orbit problem. The first step of the reduction is to compute canonical JSJ decompositions. Dehn fillings ...
• On stability conditions for the quintic threefold AI翻译
  作者：Li, Chunyi
  作者单位：University of Warwick
  摘要：We study the Clifford type inequality for a particular type of curves C-2,C-2,C-5, which are contained in smooth quintic threefolds. This allows us to prove some stronger Bogomolov-Gieseker type inequalities for Chern characters of stable sheaves and tilt-stable objects on smooth quintic threefolds. Employing the previous framework by Bayer, Bertram, Macri, Stellari and Toda, we construct an open subset of stability conditions on every smooth quintic threefold in P-C(4).