Recorded 12 February 2025. Sonja Petrovic of the Illinois Institute of Technology presents "Probability and Randomness in Nonlinear Algebra" at IPAM's Computational Interactions between Algebra, Combinatorics, and Discrete Geometry Workshop. Abstract: Many problems in symbolic computation with polynomials have high worst-case complexity. At the same time, in many areas of computational mathematics, significant improvements in efficiency have been obtained by algorithms that involve randomization, rather than deterministic ones. This talk will overview a randomized sampling framework from geometric optimization to applied computational algebra, and demonstrate its usefulness on two problems, including solving large (overdetermined) systems of multivariate polynomial equations. This talk is based on joint work with Jesus De Loera, Despina Stasi, and Shahrzad Jamshidi. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/computational-interactions-between-algebra-combinatorics-and-discrete-geometry/