PrerequisiteRepresentation theory of symmetric group, Lie groups and Lie algebrasIntroductionIn this course we will review classical invariant theory, discuss Howe duality for classical Lie groups and its extension to Lie superalgebras.We will use the dualities for classical pairs of Lie groups to pose asymptotic questions. We will study representations of these dual pairs in the limit when ran...
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...