Low Dimensional Topology and Circle-valued Morse Functions

Explore the fascinating world of hyperbolic geometry in this conference talk by Dave Futer from Temple University. Delve into the concept of the 3-dimensional Margulis constant, a universal constant with profound implications for discrete groups of isometries in hyperbolic space. Learn about the historical significance of Margulis' theorem from over 50 years ago and its applications in structural theorems of hyperbolic geometry. Follow along as Futer describes a cutting-edge, computer-assisted project aimed at determining the precise value of the Margulis constant. Discover the progress made in the symmetric case and its potential for solving the general problem through a bootstrapping argument. Gain insights into the collaborative efforts with David Gabai and Andrew Yarmola in this hour-long presentation that pushes the boundaries of our understanding of low-dimensional topology and hyperbolic geometry.