Will Perry, Undergraduate Mathematics Seminar
Consider the phenomenon of a vector space attached to each point of a shape, much as the Möbius strip can be formed by attaching a line to each point of a circle with some global “twisting”. We will see how this notion is crucial in differential geometry, is a fascinating construction in itself, and can help us understand the topology of the underlying shapes. Throughout, we will lightly touch on some fairly sophisticated algebraic and geometric ideas such as classifying spaces, representable functors, and generalised cohomology. The talk will remain accessible to those not of geometric or algebraic backgrounds.