Probability and Randomness in Nonlinear Algebra

Explore a 44-minute lecture where Sonja Petrovic from Illinois Institute of Technology delves into randomized approaches for solving complex polynomial problems at IPAM's Computational Interactions workshop. Discover how randomization techniques can improve efficiency compared to deterministic algorithms in computational mathematics. Learn about a randomized sampling framework that bridges geometric optimization and applied computational algebra, with practical applications demonstrated through two key problems, including solutions for large multivariate polynomial equation systems. Gain insights from collaborative research conducted with Jesus De Loera, Despina Stasi, and Shahrzad Jamshidi that addresses the high worst-case complexity challenges in symbolic computation with polynomials.