Challenges in Discrete Geometry - Part I- Convex Polytopes

Explore the fascinating world of convex polytopes in this 48-minute lecture by Gil Kalai from The Hebrew University of Jerusalem. Delve into the rich history and theory of face numbers in high-dimensional polytopes, starting with Euler's famous formula for 3-dimensional polytopes. Discover major combinatorial results, connections to other mathematical areas, and intriguing open problems in the field. Learn about Cauchy's rigidity theorem and its significance in the study of polytopes. Gain insights into this captivating subject that has attracted human attention since ancient times, presented as part of the Workshop on Real Algebraic Geometry and Algorithms for Geometric Constraint Systems and the Coxeter Lecture Series at the Fields Institute.