Introduced in the 1960's, BCK-algebras are the algebraic semantics of BCK-logic. Like with many algebraic structures, there is a natural way to associate a topological space to a BCK-algebra; we call this space the spectrum. In this talk I'll recall what is known about spectra of commutative BCK-algebras before asking: what happens when we drop the assumption of commutativity? The discussion will close with a conjecture about spectra of finite BCK-algebras.
On spectra of BCK-algebras
Oct. 29, 2024 2:30pm (MATH 3…
Lie Theory
Jen Gensler (CU)
X
Supercharacter theory is a construction that condenses the representation theory of an algebraic structure, hopefully without losing too much information about its representation theory while gaining combinatorial data. Nonnesting supercharacter theory considers the normal supercharacter theory of normal subgroups of UT_n associated to nonnesting set partitions or, equivalently, Dyck paths. In this talk I will define supercharacter theory and work through a motivating example leading into a discussion of results on the nonnesting supercharacter theory of UT_n.
The orthogonal/unitary calculus of Weiss is a framework of studying functors from vector spaces to topological spaces. Each such functor has an associated Taylor tower — a tower of fibrations whose layers are infinite loop spaces. When applied to the functor BO(-) or BU(-), Weiss calculus provides a "custom-made" resolution for the classifying spaces, allowing for the program of enumerating unstable vector bundles with stable calculations. In this talk, we present old and new enumeration results along this program and discuss, if time allows, an equivariant version of the story. This talk contains joint work with Hood Chatham and Morgan Opie, and work in progress with Prasit Bhattacharya.
On spectra of BCK-algebras