Explore a 22-minute IEEE conference talk delving into sum-of-squares lower bounds for the Sherrington-Kirkpatrick optimization problem. Learn about the certification problem, sum-of-squares hierarchy, and key concepts like kinetic tense problem, correction, graph matrices, spiders, and their relation to null space. Gain insights from experts Mrinalkanti Ghosh, Fernando Granha Jeronimo, Chris Jones, Aaron Potechin, and Goutham Rajendran as they discuss current knowledge, proof techniques, and open problems in this complex mathematical field.