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作者：Farkas, Gavril; Verra, Alessandro
摘要：The spin moduli space (S) over bar (g) is the parameter space of theta characteristics (spin structures) on stable curves of genus g. It has two connected components, (S) over bar (-)(g) and (S) over bar (+)(g), depending on the parity of the spin structure. We establish a complete birational classification by Kodaira dimension of the odd component (S) over bar (-)(g) of the spin moduli space. We show that (S) over bar (-)(g) is uniruled for g < 12 and even unirational for g <= 8. In this rang...
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作者：Agler, Jim; McCarthy, John E.; Young, N. J.
摘要：We fix a gap in the proof of Theorem 7.24 in Ann. of Math. 176 (2012), 1783-1826.
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作者：Zhu, Xinwen
摘要：We prove the (generalized) coherence conjecture proposed by Pappas and Rapport. As a corollary, one of their theorems, which describes the geometry of the special fibers of the local models for ramifield unitary groups, (in particular, certain line bundles and l-adic sheaves) of the global Schubert varieties, which are the equal characteristic counterparts of the local models.
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作者：Bednorz, Witold; Latala, Rafal
摘要：We present a positive solution to the so-called Bernoulli Conjecture concerning the characterization of sample boundedness of Bernoulli processes. We also discuss some applications and related open problems.
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作者：Ivanovici, Oana; Lebeau, Gilles; Planchon, Fabrice
摘要：We consider a model case for a strictly convex domain Omega subset of R-d of dimens ion d >= 2 with smooth boundary partial derivative Omega not equal 0,and we describe dispersion for the wave equation with Dirichlet boundary conditions. More specifically, we obtain the optimal fixed time decay rate for the smoothed out Green function: at l(1/4) loss occurs with respect to the boundary less case,due to repeated occurrences of swallowtail type singularities in the wave front set. :
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作者：Hochman, Michael
摘要：We study the dimension of self-similar sets and measures on the line. We show that if the dimension is less than the generic bound of min{l, s}, where 8 is the similarity dimension, then there are superexponentially close cylinders at all small enough scales. This is a step towards the conjecture that such a dimension drop implies exact overlaps and confirms it when the generating similarities have algebraic coefficients. As applications we prove Furstenberg's conjecture on projections of the ...
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作者：Helfgott, Harald A.; Seress, Akos
摘要：Given a finite group G and a set A of generators, the diameter diam(Gamma(G, A)) of the Cayley graph Gamma(G, A) is the smallest such that every element of G can be expressed as a word of length at most in AUA(-1). We are concerned with bounding diam(G) := max(A)diam((Gamma G, A)). It has long been conjectured that the diameter of the symmetric group of degree n is polynomially bounded in n, but the best previously known upper bound was exponential in, root n log n. We give a quasipolynomial u...
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作者：Marques, Fernando C.; Neves, Andre
摘要：In 1965, T. J. Willmore conjectured that the integral of the square of the mean curvature of a torus immersed in R-3 is at least 2 pi(2). We prove this conjecture using the min-max theory of minimal surfaces.
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作者：Stokman, J. V.
摘要：We derive an explicit c-function expansion of a basic hypergeometric function associated to root systems. The basic hypergeometric function in question was constructed as an explicit series expansion in symmetric Macdonald polynomials by Cherednik in case the associated twisted affine root system is reduced. Its construction was extended to the nonreduced case by the author. It is a meromorphic Weyl group invariant solution of the spectral problem of the Macdonald q-difference operators. The c...
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作者：Chen, Xiuxiong; Sun, Song
摘要：We prove that constant scalar curvature Kahler metric adjacent to a fixed Kahler class is unique up to isomorphism. The proof is based on the study of a fourth order evolution equation, namely, the Calabi flow, from a new geometric perspective, and on the geometry of the space of Kahler metrics.
