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作者：Aizenman, Michael; Duminil-Copin, Hugo
摘要：We prove that the scaling limits of spin fluctuations in four-dimensional Isingtype models with nearest-neighbor ferromagnetic interaction at or near the critical point are Gaussian. A similar statement is proven for the lambda phi(4) fields over R-4 with a lattice ultraviolet cutoff, in the limit of infinite volume and vanishing lattice spacing. The proofs are enabled by the models random current representation, in which the correlation functions deviation from Wicks law is expressed in terms...
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作者：Dimitrov, Vesselin; Gao, Ziyang; Habegger, Philipp
摘要：Consider a smooth, geometrically irreducible, projective curve of genus g >= 2 defined over a number field of degree d >= 1. It has at most finitely many rational points by the Mordell Conjecture, a theorem of Faltings. We show that the number of rational points is bounded only in terms of g, d, and the MordellWeil rank of the curve's Jacobian, thereby answering in the affirmative a question of Mazur. In addition we obtain uniform bounds, in g and d, for the number of geometric torsion points ...
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作者：Jiang, Wenshuai; Naber, Aaron
摘要：Consider a Riemannian manifold with bounded Ricci curvature vertical bar Ric vertical bar <= n - 1 and the noncollapsing lower volume bound Vol vertical bar(B-1 (p)) > v > 0. The first main result of this paper is to prove that we have the L-2 curvature bound f(B1(p)) vertical bar Rm vertical bar(2)(x) dx < C(n, v), which proves the L-2 conjecture. In order to prove this, we will need to first show the following structural result for limits. Namely, if (M-j(n),d(j), p(j)) -> (X,d,p) is a GH-li...
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作者：Jaye, Benjamin; Tolsa, Xavier; Villa, Michele
摘要：In this paper we provide a proof of the Carleson epsilon(2)-conjecture. This result yields a characterization (up to exceptional sets of zero length) of the tangent points of a Jordan curve in terms of the finiteness of the associated Carleson epsilon(2)-square function.
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作者：Fintzen, Jessica
摘要：Let k be a non-archimedean local field with residual characteristic p. Let G be a connected reductive group over k that splits over a tamely ramified field extension of k. Suppose p does not divide the order of the Weyl group of G. Then we show that every smooth irreducible complex representation of G(k) contains an .6-type of the form constructed by Kim-Yu and that every irreducible supercuspidal representation arises from Yu's construction. This improves an earlier result of Kim, which held ...
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作者：Heuts, Gijs
摘要：We consider a homotopy theory obtained from that of pointed spaces by inverting the maps inducing isomorphisms in v(n)-periodic homotopy groups. The case n = 0 corresponds to rational homotopy theory. In analogy with Quillen's results in the rational case, we prove that this v(n)-periodic homotopy theory is equivalent to the homotopy theory of Lie algebras in T(n)-local spectra. We also compare it to the homotopy theory of commutative coalgebras in T(n)-local spectra, where it turns out there ...
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作者：Brieussel, Jeremie; Zheng, Tianyi
摘要：We give a solution to the inverse problem (given a prescribed function, find a corresponding group) for large classes of speed, entropy, isoperimetric profile, return probability and L-p-compression functions of finitely generated groups. For smaller classes, we give solutions among solvable groups of exponential volume growth. As corollaries, we prove a recent conjecture of Amir on joint evaluation of speed and entropy exponents and we obtain a new proof of the existence of uncountably many p...
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作者：Dang, Nguyen-Bac; Favre, Charles
摘要：We prove that dynamical degrees of rational self-maps on projective varieties can be interpreted as spectral radii of naturally defined operators on suitable Banach spaces. Generalizing Shokurov's notion of b-divisors, we consider the space of b-classes of higher codimension cycles, and endow this space with various Banach norms. Building on these constructions, we design a natural extension to higher dimensions of the Picard-Manin space introduced by Cantat and Boucksom-Favre-Jonsson in the c...
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作者：Dac, Tuan Ngo
摘要：We study Todd-Thakur's analogues of Zagier-Hoffman's conjectures in positive characteristic. These conjectures predict the dimension and an explicit basis J(w) of the span of characteristic p multiple zeta values of fixed weight w which were introduced by Thakur as analogues of classical multiple zeta values of Euler. In the present paper we first establish the algebraic part of these conjectures which states that the span of characteristic p multiple zeta values of weight w is generated by th...
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作者：Stefanov, Plamen; Uhlmann, Gunther; Vasy, Andras
摘要：In this paper we analyze the local and global boundary rigidity problem for general Riemannian manifolds with boundary (M,g). We show that the boundary distance function, i.e., d(g)vertical bar(x)(partial derivative M)(partial derivative M), known near a point p is an element of partial derivative M at which partial derivative M is strictly convex, determines g in a suitable neighborhood of p in M, up to the natural diffeomorphism invariance of the problem. We also consider the closely related...
