ar X iv : m at h / 02 04 21 5 v 1 [ m at h . PR ] 1 7 A pr 2 00 2 Explicit Construction of the Brownian Self - Transport Operator

ar X iv : m at h / 05 04 37 3 v 1 [ m at h . Q A ] 1 9 A pr 2 00 5 Lax Operator for the Quantised Orthosymplectic

ar X iv : m at h / 02 04 28 5 v 1 [ m at h . G T ] 2 3 A pr 2 00 2 FIBER SUMS OF GENUS 2 LEFSCHETZ FIBRATIONS

Using the recent results of Siebert and Tian about the holomorphicity of genus 2 Lefschetz fibrations with irreducible singular fibers, we show that any genus 2 Lefschetz fibration becomes holomorphic after fiber sum with a holomorphic fibration.

ar X iv : m at h / 04 04 10 5 v 1 [ m at h . PR ] 5 A pr 2 00 4 What is the probability of intersecting the set of Brownian double points ?

We give potential theoretic estimates for the probability that a set A contains a double point of planar Brownian motion run for unit time. Unlike the probability for A to intersect the range of a Markov Process, this cannot be estimated by a capacity of the set A. Instead, we introduce the notion of a capacity with respect to two gauge functions simultaneously. We also give a polar decompositi...

ar X iv : m at h / 05 04 55 2 v 1 [ m at h . N T ] 2 7 A pr 2 00 5 Multiple logarithms , algebraic cycles and trees

This is a short exposition—mostly by way of the toy models " double logarithm " and " triple logarithm " —which should serve as an introduction to the article [3] in which we establish a connection between multiple polylogarithms, rooted trees and algebraic cycles.

ar X iv : m at h / 98 03 04 6 v 1 [ m at h . PR ] 1 1 M ar 1 99 8 LOCAL FIELDS , GAUSSIAN MEASURES , AND BROWNIAN MOTIONS Steven