Interlacing Polynomials

Related lectures (31)

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Explores interlacing families of polynomials and 1-sided Ramanujan graphs, focusing on their properties and construction methods.

Explores the construction of Ramanujan graphs using polynomials and addresses challenges with the probabilistic method.

Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.

Explores polynomial operations, properties, and subspaces in vector spaces.

Explores the Stein algorithm for polynomial identity testing and the minimization of a cut problem.

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Introduces linear combinations in vector spaces, operations, and polynomials of degree 2.

Covers topics related to probability and statistics, including finding specific values and significant events.

Explores interlacing families, Ramanujan graphs, and their construction using signed adjacency matrices.

Explores the theory of martingales, including conditional expectations, Chernoff bounds, and Azuma's inequality.