Explore Gromov's conjectures on scalar curvature from a general relativity perspective in this hour-long lecture. Delve into partial solutions provided by the positive mass theorem as Tin-Yau Tsang from NYU's Courant Institute examines another aspect of these influential mathematical propositions. Gain insights into the intersection of differential geometry and physics, and understand how these conjectures impact our understanding of spacetime curvature. Presented at the Institut des Hautes Etudes Scientifiques (IHES), this talk offers a deep dive into advanced mathematical concepts for researchers and enthusiasts in the field.