Searching for Hyperbolicity

Explore the concept of hyperbolicity in geometric group theory through this 52-minute AMS Invited Address given by Ruth Charney from Brandeis University at the 2018 Joint Mathematics Meetings. Delve into the fundamentals of geometric groups, presentations, and geometric objects while examining the properties of thin triangles and infinite trees. Compare and contrast hyperbolic spaces with Euclidean planes, and investigate the key characteristics that define hyperbolic properties. Gain insights into ongoing research and potential future directions in this fascinating area of mathematics.