Explore the intricacies of the HOD conjecture and its ultimate failure in this 46-minute conference talk delivered by Gabriel Goldberg at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI). Delve into the complex world of mathematical logic as part of the Workshop on "Determinacy, Inner Models and Forcing Axioms." Gain insights into the implications of this conjecture's breakdown and its significance in the field of set theory. Discover how this presentation contributes to the ongoing discourse in advanced mathematics and logic. Access the full abstract for a deeper understanding of the talk's content and context.