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作者：Corvaja, P; Zannier, U
摘要：We study the integral points on surfaces by means of a new method, relying on the Schmidt Subspace Theorem. This method was recently introduced in [CZ] for the case of curves, leading to a new proof of Siegel's celebrated theorem that any affine algebraic curve defined over a number field has only finitely many S-integral points, unless it has genus zero and not more than two points at infinity. Here, under certain conditions involving the intersection matrix of the divisors at infinity, we sh...
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作者：Pollack, R; Rubin, K
摘要：At a prime of ordinary reduction, the Iwasawa main conjecture for elliptic curves relates a Selmer group to a p-adic L-function. In the supersingular case, the statement of the main conjecture is more complicated as neither the Selmer group nor the p-adic L-function is well-behaved. Recently Kobayashi discovered an equivalent formulation of the main conjecture at supersingular primes that is similar in structure to the ordinary case. Namely, Kobayashi's conjecture relates modified Selmer group...
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作者：Bhargava, M
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作者：Navarro, G
摘要：The main problem of representation theory of finite groups is to find proofs of several conjectures stating that certain global invariants of a finite group G can be computed locally. The simplest of these conjectures is the McKay conjecture which asserts that the number of irreducible complex characters of G of degree not divisible by p is the same if computed in a p-Sylow normalizer of G. In this paper, we propose a much stronger version of this conjecture which deals with Galois automorphis...
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作者：Liverani, C
摘要：Exponential decay of correlations for C-4 contact Anosov flows is established. This implies, in particular, exponential decay of correlations for all smooth geodesic flows in strictly negative curvature.
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作者：Miyamoto, M
摘要：We give a new construction of the moonshine module vertex operator algebra V, which was originally constructed in [FLM2]. We construct it as a framed VOA over the real number field R. We also offer ways to transform a structure of framed VOA into another framed VOA. As applications, we study the five framed VOA structures on VE8 and construct many framed VOAs including V from a small VOA. One of the advantages of our construction is that we are able to construct V as a framed VOA with a positi...
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作者：Schumacher, G; Tsuji, H
摘要：By means of analytic methods the quasi-projectivity of the moduli space of algebraically polarized varieties with a not necessarily reduced complex structure is proven including the case of nonuniruled polarized varieties.
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作者：Ozsváth, P; Szabó, Z
摘要：In [27], we introduced Floer homology theories HF- (Y, s), HFinfinity (Y, s), HF+ (Y, t), (HF) over cap (Y, s),and HFred (Y, s) associated to closed, oriented three-manifolds Y equipped with a Spin(c) structures s is an element of Spin(c)(Y). In the present paper, we give calculations and study the properties of these invariants. The calculations suggest a conjectured relationship with Seiberg-Witten theory. The properties include a relationship between the Euler characteristics of HF+/- and T...
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作者：Benjamini, I; Kesten, H; Peres, Y; Schramm, O
摘要：The uniform spanning forest (USF) in Z(d) is the weak limit of random, uniformly chosen, spanning trees in [-n, n]. Pemantle [11] proved that the USF consists a.s. of a single tree if and only if d <= 4. We prove that any two components of the USF in Zd are adjacent a.s. if 5 <= d <= 8, but not if d >= 9. More generally, let N(x, y) be the minimum number of edges outside the USF in a path joining x and y in Zd. Then max{N(x,y): x, y epsilon Z(d)} = [(d - 1)/4] a.s. The notion of stochastic dim...
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作者：Kuwert, E; Schätzle, R
摘要：We investigate point singularities of Willmore surfaces, which for example appear as blowups of the Willmore flow near singularities, and prove that closed Willmore surfaces with one unit density point singularity are smooth in codimension one. As applications we get in codimension one that the Willmore flow of spheres with energy less than 8pi exists for all time and converges to a round sphere and further that the set of Willmore tori with energy less than 8pi - delta is compact up to Mobius...
