Polynomial Optimization: Theory and Applications

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Related lectures (34)

Stein Algorithm: Polynomial Identity Testing

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

Algebraic Curves: Normalization

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Complex Roots: Conjugate Pairs and Quadratic Equations

Explores complex roots, conjugate pairs, and quadratic equations solving strategies.

Polynomial Identity Testing

Covers polynomial identity testing using oracles and random point evaluation, with applications in graph theory and algorithmic aspects.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Bar Construction: Homology Groups and Classifying Space

Covers the bar construction method, homology groups, classifying space, and the Hopf formula.

Decomposition: Simple and Quadratic Factors MOOC: Analysis I MOOC: Analysis I (part 7) : Indefinite and definite integrals, integration (selected chapters)

Explores the decomposition of a function into simple and quadratic factors.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Equations: Degree and Solutions

Explores polynomial equations, their degree, solutions, and domain definition.

Analyse 2: Division euclidienne

Explores the process of division euclidienne in polynomials, emphasizing the importance of polynomial degrees during operations.

Polynomial Optimization: SOS and Nonnegative Polynomials Log in to Mediaspace to watch this video

Explores polynomial optimization, emphasizing SOS and nonnegative polynomials, including the representation of polynomials as quadratic functions of monomials.

Error Analysis and Interpolation Log in to Mediaspace to watch this video

Explores error analysis and limitations in interpolation on evenly distributed nodes.

Characteristic Polynomials and Similar Matrices Log in to Mediaspace to watch this video

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Complex Roots and Polynomials Log in to Mediaspace to watch this video

Explores complex roots, polynomials, and factorizations, including roots of unity and the fundamental theorem of algebra.

Algebraic Geometry: Forms and Maps Log in to Mediaspace to watch this video

Covers the concept of forms in algebraic geometry and the implications of constructing Bloch(A) from glued copies of A.

Tori: Character Forms and Monomials Log in to Mediaspace to watch this video

Explores Tori in algebraic geometry, emphasizing character forms and monomials.

Irreducible Polynomials: Degree and Roots Log in to Mediaspace to watch this video

Explores irreducible polynomials, focusing on their degree and roots in different fields.

Complex Numbers: Argument and Polar Method Log in to Mediaspace to watch this video

Introduces the argument of complex numbers and the polar method, demonstrating their application in finding roots.

Directed Networks & Hypergraphs Log in to Mediaspace to watch this video

Explores directed networks with asymmetric relationships and hypergraphs that generalize graphs by allowing edges to connect any subset of nodes.

Polynomials: Definitions and Operations Log in to Mediaspace to watch this video

Covers the definition and operations of polynomials, including addition and multiplication, degree, coefficients, and their role in algebraic systems.

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