I will present a version of Hochschild and cyclic homology that may be closely related to algebraic K-theory. This is partly based on old ideas of J.-L. Loday, C.Ogle, and myself. Time permitting, I will outline some conjectural applications, for example to K-theory of cluster algebras.

Bio: Boris Tsygan is an American mathematician. He earned his PhD from Moscow State University in 1987 under supervision of Yuri Manin. He had Harvard Prize Fellowship at Harvard in 1989-90, was Associate Professor at Penn State in 1990-94, Professor at Penn State in 1994-2001, and since then is is a Professor at Northwestern. His research is in the fields of noncommutative geometry, K-theory, and deformation quantization.