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Explore the profound connection between quantum field theory and lattice models in this comprehensive lecture. Delve into the long-standing challenge of defining topological operators on lattice structures, a crucial aspect in both condensed matter and high energy physics. Discover how higher category theory provides an unexpected yet elegant solution to this problem, offering new insights into the relationship between continuum and lattice quantum field theories. Learn about the historical context, including the successful resolution of vortices in the Villain model and the ongoing challenges with instantons in lattice QCD. Gain a deeper understanding of how seemingly abstract mathematical concepts become physically intuitive when applied to lattice models, potentially revolutionizing our approach to non-perturbative physics and numerical computations.
