Explore the intricacies of certifying nonnegativity in real algebraic geometry during this 58-minute seminar presented by Timo de Wolff from Technische Universität Braunschweig. Delve into the historical context of nonnegativity certification, focusing on sums of squares (SOS) and the more recent sums of nonnegative circuit polynomials (SONC). Discover the applications of these concepts in polynomial optimization and theoretical computer science. Examine the theoretical bounds for hierarchies applied to optimization problems on the Boolean Hypercube, including standard problems like Maxcut and Knapsack. Gain insights into nonconvex optimization, nonnegative polynomials, and dual hierarchies through this comprehensive presentation moderated by Jose Israel Rodriguez from the University of Wisconsin-Madison.