Title: Geometric Flows and Low Dimensional Topology -- recent achievements and current efforts.
Abstract:
We dedicate the first part of our talk to introduce the Ricci flow. We begin by defining the Ricci flow. We then provide some heuristics -- why could one expect it to homogenize spaces. We will then give a bird’s-eye view of a wonderful theorem proven using the flow -- the generalized Smale conjecture. We will try to highlight interesting traits of the Ricci flow that are crucial for the proof.
In the second part of our talk, we will consider an extrinsic analogue; We inspect Smale's theorem from the perspective of embeddings. We'll then introduce the Mean Curvature Flow. Lastly, we'll describe how we hope to use the MCF in a proof for Smale's theorem.