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Explore the fundamental concepts and applications of lattice theory in this comprehensive lecture by Daniele Micciancio from UC San Diego. Delve into the basic mathematics of lattices, their algorithmic properties, complexity considerations, and cryptographic implications. Gain insights into the core principles that underpin lattice-based cryptography and its role in modern security systems. Discover how lattices intersect with various fields of mathematics and computer science, providing a solid foundation for understanding advanced topics in cryptography and computational complexity.