Abstract: We study various properties of finite algebras and the varieties they generate. In particular, we look for counterexamples to the conjecture that every dualizable algebra is finitely based.

Abstract: Abstract for Talk

Abstract: Abstract for Talk

Abstract: Abstract for Talk

Abstract: Abstract for Talk

Abstract: Abstract for Talk

Abstract: In this talk I will introduce BCK-algebras and discuss some of their universal algebraic properties. In the bounded commutative case, I will develop the beginnings of a Priestley duality for BCK-algebras and discuss some complications.

Abstract: Every invertible automaton with finitely many states produces a group of automorphisms of a regular rooted tree. In this talk, we outline how to obtain a group from an automaton and then discuss a particular family of examples.

Abstract: An early result in the theory of Natural Dualities is that an algebra with a near unanimity (NU) term is dualizable. A converse to this is also true: if V(A) is congruence distributive and A is dualizable, then A has an NU term. An important generalization of the NU term for congruence distributive varieties is the cube term for congruence modular (CM) varieties, and it has been thought that a similar characterization of dualizability for algebras in a CM variety would also hold. We prove that if A omits tame congruence types 1 and 5 (all locally finite CM varieties omit these types) and is dualizable, then A has a cube term.

Abstract: Totally disconnected, locally compact (t.d.l.c.) groups are a large class of topological groups that arise from a few different sources, for instance as automorphism groups of combinatorial structures, or from the study of isomorphisms between finite index subgroups of a given group. Two analogies are that they are like 'discrete groups combined with compact groups' or 'non-Archimedean Lie groups'. A general theory has begun to emerge in recent years, in which we find that the interaction between small-scale and large-scale structure in t.d.l.c. groups is somewhere between the two extremes that these analogies would suggest. I will give a survey of some ways in which these groups arise and a few recent results in the area.

Abstract: This is an update on my research on the maximal subgroup growth of certain f.g. groups. The focus is on metabelian groups, virtually abelian groups, and on the Baumslag-Solitar groups.

Abstract: Abstract for Talk

Abstract: A mode is an algebra which is idempotent and whose basic operations are homomorphisms. The main focus of this talk will be to give a generalization of Jezek and Kepka's embedding theorem for groupoid modes. We will show that a mode is embeddable into a subreduct of a semimodule over a commutative semiring if and only if it satisfies the so called Szendrei identities. Thus the operations on Szendrei modes can be represented in a particularly nice way. This will involve thinking of operations “additively”, that is, taking an n-ary operation and considering it as a sum of n unary operations.