2 1 Ju n 20 05 UNIQUENESS OF E ∞ STRUCTURES FOR CONNECTIVE COVERS

ar X iv : h ep - t h / 05 06 19 5 v 1 2 3 Ju n 20 05 Geometric transitions and mixed Hodge structures

We formulate and prove a B-model disc level large N duality result for general conifold transitions between compact Calabi-Yau spaces using degenerations of Hodge structures.

ar X iv : h ep - p h / 05 06 11 1 v 2 1 4 Ju n 20 05 Transverse positron polarization in the μ + → e + ν̄ μ ν e decay in

Ju n 20 07 On pathwise uniqueness for reflecting Brownian motion in C 1 + γ domains ∗ Richard F . Bass and Krzysztof Burdzy

Pathwise uniqueness holds for the Skorokhod stochastic differential equation in C 1+γ-domains in R d for γ > 1/2 and d ≥ 3.

3 0 Ju n 20 05 Families of Painlevé VI equations having a common solution

We classify all functions satisfying non-trivial families of PVIα equations. It turns out that all of these 23 solutions are of geometric origin: they are related to deformations of elliptic surfaces as proved earlier by Doran. Similarly, we prove that the same solutions can be obtained from deformations of three-sheeted covers of P1 with branching locus consisting of four points. e-mail: basse...

. D S ] 2 9 Ju n 20 05 Dimensions of Julia sets of expanding rational semigroups ∗

We estimate the upper box and Hausdorff dimensions of the Julia set of an expanding semigroup generated by finitely many rational functions, using the thermodynamic formalism in ergodic theory. Furthermore, we show Bowen’s formula, and the existence and uniqueness of a conformal measure, for a finitely generated expanding semigroup satisfying the open set condition.