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作者：Fox, Jacob
摘要：Let H be a fixed graph with h vertices. The graph removal lemma states that every graph on n vertices with o(n(h)) copies of H can be made H-free by removing o(n(2)) edges. We give a new proof which avoids Szemeredi's regularity lemma and gives a better bound. This approach also works to give improved bounds for the directed and multicolored analogues of the graph removal lemma This answers questions of Alon and Gowers.
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作者：Furusho, Hidekazu
摘要：It is proved that Drinfelid's pentagon equation implies the generalized double shuffle relation. As a corollary, an embedding from the Grothen-dieck-Teichmuller group GRT(1) into Racinet's double shuffle group DMR0 is obtained, which settles the project of Deligne-Terasoma. It is also proved that the gamma factorization formula follows from the generalized double shuffle relation.
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作者：Feray, Valentin; Sniady, Piotr
摘要：We prove an upper bound for characters of the symmetric groups. In particular, we show that there exists a constant a > 0 with a property that for every Young diagram lambda with n boxes, r(lambda) rows and c(lambda) columns vertical bar Tr rho(lambda)(pi)/Tr rho(lambda)(e)vertical bar <= [a max (r(lambda)/n, c(lambda)/n, vertical bar pi vertical bar/n)](vertical bar pi vertical bar), where vertical bar pi vertical bar is the minimal number of factors needed to write pi is an element of S-n as...
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作者：Jaikin-Zapirain, Andrei; Pyber, Laszlo
摘要：We obtain a surprisingly explicit formula for the number of random elements needed to generate a finite d-generator group with high probability. As a corollary we prove that if G is a d-generated linear group of dimension n then cd + log n random generators suffice. Changing perspective we investigate profinite groups F which can be generated by a bounded number of elements with positive probability. In responses to a question of Shalev we characterize such groups in terms of certain finite qu...
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作者：Favre, Charles; Jonsson, Mattias
摘要：We find good dynamical compactifications for arbitrary polynomial mappings of C-2 and use them to show that the degree growth sequence satisfies a linear integral recursion formula. For maps of low topological degree we prove that the Green function is well behaved. For maps of maximum topological degree, we give normal forms.
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作者：Li, Xiaoqing
摘要：In this paper, we will give the subconvexity bounds for self-dual GL(3) L-functions in the t aspect as well as subconvexity bounds for self-dual GL(3) x GL(2) L-functions in the GL(2) spectral aspect.
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作者：Brubaker, Ben; Bump, Daniel; Friedberg, Solomon
摘要：We show that the Whittaker coefficients of Borcl Eisenstein series on the metaplectic covers of GL(r+1) can be described as multiple Dirichlet series in r complex variables, whose coefficients are computed by attaching a number-theoretic quantity (a product of Gauss sums) to each vertex in a crystal graph. These Gauss sums depend on string data previously introduced in work of Lusztig, Berenstein and Zelevinsky, and Littelmann. These data are the lengths of segments in a path from the given ve...
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作者：Dasgupta, Samit; Darmon, Henri; Pollack, Robert
摘要：Let F be a totally real field and x an abelian totally odd character of F. In 1988, Gross stated a p-adic analogue of Stark's conjecture that relates the value of the derivative of the p-adic L-function associated to x and the p-adic logarithm of a p-unit in the extension of F cut out by x. In this paper we prove Gross's conjecture when F is a real quadratic field and x is a narrow ring class character. The main result also applies to general totally real fields for which Leopoldt's conjecture...
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作者：Gurevich, Shamgar; Hadani, Ronny
摘要：In this paper we present a proof of the Hecke quantum unique ergodicity rate conjecture for the Hannay-Berry model of quantum mechanics on the two-dimensional torus. This conjecture was stated in Z. Rudnick's lectures at MSRI, Berkeley 1999, and ECM, Barcelona 2000.
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作者：Arnaud, Marie-Claude
摘要：We consider the irrational Aubry-Mather sets of an exact symplectic monotone C-1 twist map of the two-dimensional annulus, introduce for them a notion of C-1-regularity (related to the notion of Bouligand paratingent cone) and prove that a Mather measure has zero Lyapunov exponents if and only if its support is C-1-regular almost everywhere; a Mather measure has nonzero Lyapunov exponents if and only if its support is C-1-irregular almost everywhere; an Aubry-Mather set is uniformly hyperbolic...
