Abstract These lectures will explore connections between (generalized) q-Schur algebras and the quantized enveloping algebra Uq(g) associated with a simple Lie algebra g. These connections are facilitated by a certain completion of Lusztig’s modified form of Uq(g). Although the q-Schur algebras arose initially as quotients of Uq(g) it is possible to reverse history and use them as a tool to re...
Record: NoLevel: GraduateLanguage: EnglishPrerequisiteAlgebraic geometry (background in algebraic number theory will be helpful)AbstractPrismatic cohomology, which is developed in a recent work of Bhatt-Scholze, is a cohomology theory for schemes over p-adic rings. It is considered to be an overarching cohomology theory in p-adic geometry, unifying etale, de Rham, and crystalline cohomology. Du...