WWDC26：2026 年 6 月 8 日至 12 日 (太平洋时间)

In this paper we prove, that none of the three combinatorial 8- manifolds on 15 vertices constructed by Brehm and Kuhnel, each of which is a cohomology quaternionic projective plane, can be combinatorially embedded in the Euclidean 12-space, though they have tight polyhedral embeddings in Euclidean 14-space. This extends a similar method already known for the nonembeddings of real and complex projective planes.

本刊讯 由中国商务部、法兰西共和国外贸部作为特别支持单位．法国勒阿弗尔（LEHAVRE）大区经济发展委员会主办，法国玻格瑟曼国际商务会展有限公司、北京玻格瑟曼国际商务会展服务有限公司、法国法中企业家与管理者协会（ASSOGES）共同承办的”欧中首届外贸、招商引资项目对接会（CHINA EUROPA）”．将于2006年12月6日至8日在法国第一大港口城市勒阿弗尔举行。

It is shown that the percolation model of hydrogen-bonded crystals, which is a 6-vertex model with bond defects, is completely equivalent with an 8-vertex model in an external electric field. Using this equivalence we solve exactly a particular 6-vertex model with bond defects. The general solution for the Bethe-like lattice is also analyzed.

We review some of the recent progress on the scaling limit of two-dimensional critical percolation; in particular, the convergence of the exploration path to chordal SLE(6) and the "full" scaling limit of cluster interface loops. The results given here on the full scaling limit and its conformal invariance extend those presented previously. For site percolation on the triangular lattice, the results are fully rigorous. We explain some of the main ideas, skipping most technical details.