Lectures related to String duality

Covers the black pobrane solution in D dimensions with charged probrane and extremal pobrate.

Covers the concept of holography in classical gravity and its relation to string theory.

Explores optimization duality, weak and strong duality, practical optimization algorithms, and challenges in nonconvex-concave problems.

Covers the proof of strong duality in optimization problems and provides examples of Rayleigh quotient optimization.

Explores scaling and renormalization in statistical mechanics, emphasizing critical points and invariant properties.