Differential Geometry

AY2021/2022 Semester 2

This course will introduce the mathematical framework and most important fundamental concepts of classical Differential Geometry. Differential Geometry is the mathematical study of geometric shapes using tools from analysis such as calculus and differential forms. The ideas and tools are important not just in pure mathematics but play a fundamental role in many areas of physics such as general relativity and gauge theory, and in diverse parts of Engineering such as robotics and computational geometry. The course aims to give you a foundational understanding in the most important topics within Differential Geometry. 1. The mathematical machinery of differential forms. 2. The classical theory of curves and embedded surfaces. 3. First steps towards abstract Riemannian geometry. The aim is for you to be sufficiently prepared to continue deeper study in this topic and also to equip you so that when you encounter these ideas in different topics (such as in physics or in Engineering) then you have the ability to bring in an expert understanding of the theory and the ability to deepen your learning as is needed in the context