On the Shapes of Rational Lemniscates

Explore the geometric properties and mathematical structures of rational lemniscates in this 59-minute conference talk delivered by Kirill Lazebnik from the University of Texas at Dallas at the Fields Institute. Delve into the intricate shapes and characteristics of these mathematical curves, which are generalizations of the classical lemniscate of Bernoulli, as part of the Fields-CNAM Nonlinear Days 2025 conference focusing on dynamical, geometric, and random structures and processes. Gain insights into advanced topics in algebraic geometry and complex analysis through this specialized mathematical presentation that examines how rational functions generate these fascinating curve families and their topological properties.