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Closest Vector Problem: Voronoi Cells
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Related lectures (56)
Convergence of Random Walks
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Explores the convergence of random walks on graphs and the properties of weighted adjacency matrices.
Preliminaries in Measure Theory
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Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.
Joint Equidistribution of CM Points
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Covers the joint equidistribution of CM points and the ergodic decomposition theorem in compact abelian groups.
Caratheodory Bounds: Integer Programming
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Covers Caratheodory bounds for integer programming, focusing on linear programming and the existence of optimal solutions.
Inductive Propositions: Reasoning and Evaluation Techniques
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Discusses inductive propositions, their definitions, and applications in reasoning and evaluation techniques in Coq.
Cauchy-Hadamard Theorem
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Explores the Cauchy-Hadamard theorem on convergence radius of power series and real analytical solutions.
Quantum Dynamics: Spectral Decomposition
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Explores the spectral decomposition of Hilbert space and its implications in quantum dynamics.
Integer Cones
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Covers the concept of integer cones and Carathéodory's theorem with illustrative examples.
Relative Homology: Exact Sequence
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Covers the long exact sequence of relative homology groups and chain complexes.
Interlacing Families and Ramanujan Graphs
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Explores interlacing families, Ramanujan graphs, and their construction using signed adjacency matrices.
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Hadamard Factorisation
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Covers the Hadamard factorisation theorem for entire functions of order at most 1.
Introduction to Analysis
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Covers the basics of analysis, including proofs, sets, rational and real numbers, and the concept of infimum.
Proof of Strong Duality
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Covers the proof of strong duality in optimization problems and provides examples of Rayleigh quotient optimization.
Induced Homomorphisms on Relative Homology Groups
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Covers induced homomorphisms on relative homology groups and their properties.
Lipschitz Maps and Compact Domains
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Covers Lipschitz maps, compact domains, changing variables, counting problems, and probability of ideals.
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