A variety is Hobby-McKenzie if it satisfies an idempotent Mal’tsev condition that fails in semilattices. Such varieties form a Mal’tsev class which resembles that of Taylor varieties: the idempotent condition can be chosen to be a set of linear identities in two variables. For locally finite varieties, this class contains precisely the varieties omitting TCT types 1 and 5. In this talk, we provide a characterization of general (not necessarily locally finite or idempotent) Hobby-McKenzie varieties based on their compatible 3-ary relations. As a consequence, we prove that these varieties form a prime filter in the interpretability lattice of varieties. We also propose a nice characterization that depends instead on the compatible digraphs of the variety, but which is only proven to be correct in the locally finite case. Joint work with B. Bodor, M. Maróti and L. Zádori
On general Hobby-McKenzie varieties
Tue, Nov. 5 3:30pm (MATH 3…
Topology
Taylor Rogers
X
This semester we have introduced chromatic homotopy theory and the modern formulation of algebraic K-theory. In this talk, we will discuss chromatic redshift, a recently proven result that describes a way in which chromatic homotopy theory and algebraic K-theory interact. This interaction is an important ingredient in the recent disproof of the longstanding telescope conjecture.
On general Hobby-McKenzie varieties