Using Abstract Networks to Study Symmetry

歌剧是一种数学工具，用来包装离散的信息块之间的联系。换句话说，歌剧是一种网络，特别适合通过将复杂问题分解为更小的、可管理的数据包来处理复杂问题。这个项目的目的是重新想象几何和拓扑学中的经典物体，如Teichmüler空间，作为无穷大歌剧的变体。这种重新想象将确保对三个数学领域的关键对象有新的见解：代数数论(现代加密的数学)、量子群的表示理论和拓扑量子场论。

An operad is a mathematical tool for packaging the connection between discrete blocks of information. In other words, an operad is a type of network, particularly suited for approaching complex problems by breaking them into smaller, manageable packets. This project aims to reimagine classical objects in geometry and topology such as Teichmüller space as variations of infinity operads. This reimagining will ensure new insights into key objects across three areas of mathematics: algebraic number theory (the mathematics of modern encryption), the representation theory of quantum groups and topological quantum field theories.