Explore the intersection of supersymmetric compactifications and arithmetic properties of Calabi-Yau manifolds in this focused mathematical lecture. Delve into advanced topics in algebraic geometry and theoretical physics as the speaker examines how SUSY compactifications relate to the arithmetic structure of these special geometric objects. Learn about the mathematical foundations underlying string theory compactifications and their connections to number theory through the lens of Calabi-Yau varieties. Gain insights into current research developments in this specialized area where differential geometry, algebraic geometry, and mathematical physics converge. The presentation forms part of a focused meeting series dedicated to advancing understanding of Calabi-Yau varieties and their applications in modern mathematics and theoretical physics.