U.S.-Czech Mathematics Research on Homotopy Invariant Algebraic Structures

这个美国-捷克数学项目是北卡罗莱纳州立大学的托马斯·拉达和北卡罗莱纳州立大学的詹姆斯·斯塔舍夫以及布拉格的同行捷克科学院数学研究所的马丁·马克尔的合作成果。他们的目标是澄清各种代数结构的同伦不变性。为此，他们打算利用操作数来研究几种代数环境下的同伦不变性问题。虽然拓扑环境下的同伦不变结构已经得到了很好的研究，但代数环境下的类似问题仍然需要关注。这个美国-捷克团队研究的问题涉及强同伦代数的范畴及其同伦理论性质。如果成功，他们的研究将把这些想法与数学物理中出现的几个复杂的代数结构结合起来。研究结果将为微扰理论和变形量化的跨学科发展奠定理论基础。这个国际拓扑学项目实现了推进科学知识的计划目标，使美国和中欧的专家能够在共同感兴趣和能力强的领域结合互补的人才和共享研究资源。

This U.S.-Czech mathematics project is a cooperative effort between Thomas Lada at North Carolina State University and James Stasheff of the University of North Carolina with their counterpart in Prague, Martin Markl at the Mathematical Institute of the Czech Academy of Sciences. Their goal is to clarify the homotopy invariance properties of various algebraic structures. To do so they intend to utilize operads to study the question of homotopy invariance in several algebraic settings. While homotopy invariant structures in the topological setting have been well studied, similar questions in algebraic settings still require attention. The problems to be investigated by this U.S.-Czech team deal with the category of strongly homotopy algebras and their homotopy theoretic properties. If successful, their investigation will integrate these ideas with several sophisticated algebraic structures that arise in mathematical physics. Results should improve the theoretical underpinning for cross-disciplinary advances in perturbation theory and deformation quantization. This international project in topology fulfills the program objective of advancing scientific knowledge by enabling experts in the United States and Central Europe to combine complementary talents and share research resources in areas of strong mutual interest and competence.