IntroductionThe classical theory of algebraic geometry connects geometric concepts with corresponding notions in commutative algebra. In the recent decades there was an interest in building a parallel theory based on associative (non-commutative) algebras. We will discuss the basic ideas of this developing theory mostly following Ginzburg's lectures as well as several more recent papers.The cla...
IntroductionScattering amplitudes sit at the intersection of experimental physics, theoretical physics, and pure mathematics. Besides being directly useful at particle colliders or gravitational wave detectors, their surprising simplicity revealed symmetries and dualities hidden by traditional Lagrangian perspectives, and hints towards a completely new approach to quantum field theory.This cour...