Discrete Geometric Analysis — Mathematics that Connects Micro and Macro Worlds

As a common language for describing our universe, mathematics has contributed to the development of science throughout its long history. People have proposed mathematical models that describe the shapes and movements of the natural world and have developed mathematics as necessary. As our knowledge and interests have expanded and new sciences have emerged, mathematics has been given the opportunity to develop and evolved.

As observation and measurement techniques have become more sophisticated in recent years, it has become clear that the materials we see in everyday life are composed of very small units called atoms, which are connected to each other through interactions to form networks. It has also become evident that networks comprising networks form more complex microscopic worlds and that such networks determine the properties of materials. This has increased the need for mathematics in order to understand the relationship between the microscopic world and the macroscopic properties of materials we see and touch every day. Discrete geometric analysis reveals such hierarchical networks and the relationships between hierarchies. At the symposium, the speaker will discuss the challenges that discrete geometric analysis addresses with specific examples.