Hopf-Cyclic (Co)Homology

Atabey Kaygun, Ohio State University

Abstract. Starting from how algebra and geometry interact, I will explain how Hopf algebras arose as natural objects for studying symmetries of non-commutative spaces whose algebra of coordinate functions are non-commutative. I will also explain what Hochschild and cyclic cohomology of algebras are, in both conceptual and computational terms, and then describe how these cohomology theories are affected in the presence of a Hopf symmetry.