Mathematics of Computation Through the Lens of Linear Equations and Lattices

Mathematics of Computation Through the Lens of Linear Equations and Lattices

Explore the mathematics of computation through the lens of linear equations and lattices in this 45-minute lecture by Muli Safra. Delve into topics such as error-correcting codes, the Closest Vector Problem, and unique games. Examine lattices as discrete subgroups and their role in computational problems. Investigate the relationship between worst-case and average-case scenarios, and learn about Minkowski's theorem and its reverse. Discover open questions related to classical problems and the hardness of approximating SVP/CVP. Gain insights into the potential future of computing while exploring the intricate connections between linear algebra, geometry, and computational complexity.