Lectures related to Hilbert series and Hilbert polynomial

Polynomial Optimization: Theory and Applications

Explores polynomial optimization, emphasizing sum-of-squares polynomials and their applications, including monomial representation and theorem proofs.

Polynomial Optimization: SOS and Nonnegative Polynomials

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

Renormalization of Gauge Theories

Covers the renormalization of gauge theories and composite operators.

Adjunctions and Applications

Covers adjunctions, projective varieties, regularity, and valuative criteria in algebraic geometry.

Vector spaces: Hilbert space

Introduces vector spaces, bases, and the Hilbert space, highlighting the practical implications of defining a basis in a vector space.

Simon Problem: Quantum Algorithm and Hilbert Space

Covers Simon's quantum algorithm, unitary operations, and the Simon problem.