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作者：Erdos, Laszlo; Schlein, Benjamin; Yau, Horng-Tzer
摘要：Consider a system of N bosons in three dimensions interacting via a repulsive short range pair potential (NV)-V-2 (N(xi - xj)), where x = (x(1),...,x(N)) denotes the positions of the particles. Let H-N denote the Hamiltonian of the system and let psi(N,t) be the solution to the Schrodinger equation. Suppose that the initial data psi(N,0) satisfies the energy condition <= C-k N-k or k = 1, 2,.... We also assume that the k-particle density matrices of the initial state are asymptotically factori...
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作者：Ruelle, David
摘要：The Lee-Yang circle theorem describes complex polynomials of degree n in z with all their zeros on the unit circle vertical bar z vertical bar = 1. These polynomials are obtained by taking z(1) = ... = z(n) = z in certain multiaffine polynomials Psi(z(1),...,z(n)) which we call Lee-Yang polynomials (they do not vanish when vertical bar z(1)vertical bar,..., vertical bar z(n)vertical bar < 1 or vertical bar z(1)vertical bar,...,vertical bar z(n)vertical bar > 1). We characterize the Lee-Yang po...
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作者：Mauduit, Christian; Rivat, Joel
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作者：Cheeger, Jeff; Kleiner, Bruce
摘要：This is one of a series of papers examining the interplay between differentiation theory for Lipschitz maps X -> V and bi-Lipschitz nonembeddability, where X is a metric measure space and V is a Banach space. Here, we consider the case V = L-1, where differentiability fails. We establish another kind of differentiability for certain X, including R-n and H, the Heisenberg group with its Carnot-Caratheodory metric. It follows that H does not bi-Lipschitz embed into L-1, as conjectured by J. Lee ...
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作者：Mossel, Elchanan; O'Donnell, Ryan; Oleszkiewicz, Krzysztof
摘要：In this paper we study functions with low influences on product probability spaces. These are functions f : Omega(1) x ... Omega(n) -> R that have E[Var(Omega i) [f]] small compared to Var[f] for each i. The analysis of boolean functions f : {-1, 1}(n) -> {-1, 1} with low influences has become a central problem in discrete Fourier analysis. It is motivated by fundamental questions arising from the construction of probabilistically checkable proofs in theoretical computer science and from probl...
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作者：Bernstein, Joseph; Reznikov, Andre
摘要：We describe a new method to estimate the trilinear period on automorphic representations of PGL(2)(R). Such a period gives rise to a special value of the triple L-function. We prove a bound for the triple period which amounts to a subconvexity bound for the corresponding special value of the triple L-function. Our method is based on the study of the analytic structure of the corresponding unique trilinear functional on unitary representations of PGL(2)(R).
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作者：Lin, Chang-Shou; Wang, Chin-Lung
摘要：We show that the Green functions on flat tori can have either three or five critical points only. There does not seem to be any direct method to attack this problem. Instead, we have to employ sophisticated nonlinear partial differential equations to study it. We also study the distribution of the number of critical points over the moduli space of flat tori through deformations. The functional equations of special theta values provide important inequalities which lead to a solution for all rho...
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作者：Venkatesh, Akshay
摘要：We introduce a geometric method to bound periods of automorphic forms. The key features of this method are the use of equidistribution results in place of mean value theorems, and the systematic use of mixing and the spectral gap. Applications are given to equidistribution of sparse subsets of horocycles and to equidistribution of CM points; to subconvexity of the triple product period in the level aspect over number fields, which implies subconvexity for certain standard and Rankin-Selberg L-...
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作者：Kim, Minhyong
摘要：We show how the finiteness of integral points on an elliptic curve over Q with complex multiplication can be accounted for by the nonvanishing of L-functions that leads to bounds for dimensions of Selmer varieties.
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作者：Osin, Denis
摘要：We generalize the small cancellation theory over ordinary hyperbolic groups to relatively hyperbolic settings. This generalization is then used to prove various embedding theorems for countable groups. For instance, we show that any countable torsion free group can be embedded into a finitely generated group with exactly two conjugacy classes. In particular, this gives the affirmative answer to the well-known question of the existence of a finitely generated group G other than Z/2Z such that a...
