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

这个美国-捷克数学项目是北卡罗来纳州州立大学的托马斯拉达和北卡罗来纳州大学的詹姆斯·斯塔谢夫与他们在布拉格的同行、捷克科学院数学研究所的马丁·马克尔之间的合作努力。 他们的目标是阐明各种代数结构的同伦不变性。 要做到这一点，他们打算利用运算来研究同伦不变性的问题，在几个代数设置。 虽然同伦不变结构的拓扑设置已经得到了很好的研究，类似的问题在代数设置仍然需要注意。 这个美国要调查的问题-捷克研究组研究了强同伦代数范畴及其同伦理论性质。 如果成功的话，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。 结果应改善微扰理论和变形量子化的跨学科进展的理论基础。 这个国际拓扑学项目通过使美国和中欧的专家能够联合收割机互补人才并在相互感兴趣和有能力的领域共享研究资源，实现了推进科学知识的计划目标。

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.