Applied Topology

这一研究项目的主要目标是在几个方面推动应用拓扑学学科的发展，总体上取得重大进展。我们计划在两个主要方向上工作：组合扭转和规避，以及并发拓扑。在第一个方向，我们计划通过使用一种新的策略来接近该领域的一个主要猜想来加强组合代数拓扑的理论基础。在第二个方向，我们想要结合并发和理论分布式计算的现有发展，从而发展我们所称的知识-边的拓扑。这里还有一些我们计划攻击的显式猜想。整个项目充斥着数量拓扑学的思想，其中实际的单纯细分特别重要。

The main objective of this research project is to drive forward the subject of Applied Topology on several fronts, providing a major advancement as a total result. We propose to work in 2 main directions: combinatorial torsions and evasiveness, and topology in concurrency.In the first direction, we plan to strengthen the theoretical foundations of combinatorial alge- braic topology by using a novel strategy to approach a major conjecture in the field.In the second direction, we want to bring together the existing developments on concurrency and theoretical distributed computing and thus develop what we call the topology of knowl- edge. Also here there is a number of explicit conjectures which we plan to attack.The whole project is suffused with ideas of quantitative topology, where the actual simplicial subdivision gains special importance.