Using Abstract Networks to Study Symmetry

运算符是一种数学工具，用于封装离散信息块之间的连接。换句话说，操作是一种网络类型，特别适合于通过将复杂问题分解成更小的、可管理的数据包来处理复杂问题。该项目旨在重新想象几何和拓扑中的经典物体，如teichm<s:1> ller空间，作为无限操作数的变化。这种重新构想将确保对数学三个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.