Logic Seminar Abstracts

	Logic Seminar Abstracts
	Title: Clones of algebras with parallelogram terms. Speaker: Keith Kearnes Affiliation: CU Time: 3pm, Monday, September 11 Location: Math 220 Abstract: This is a report on a paper by Ágnes Szendrei and myself, which characterizes the clones of algebras with a `parallelogram term'. This is a new type of term, which generalizes a Maltsev term and a near unanimity term. I will prove that an algebra has a parallelogram term if and only if it has a `k-cube term', something first defined last year in a paper by Berman, Idziak, Markovic, McKenzie, Valeriote and Willard. Title: Clones of algebras with parallelogram terms. Speaker: Kearnes Affiliation: CU Time: 3pm, Monday, September 18, 25, October 2, 16, 23 Location: Math 220 Abstract: The continuation of the previous talk. Title: Polynomial clones on groups. Speaker: Peter Mayr Affiliation: Johannes Kepler Universität, Linz Time: 3pm, Monday, November 6 Location: Math 220 Abstract: Two algebras on a fixed set are called polynomially equivalent if their clones of polynomial functions are equal. Even for algebras that have a group reduct, in general, equality of the k-ary polynomial functions for a fixed k does not imply polynomial equivalence. I will talk about a class of expansions of groups whose clones of polynomial functions are determined by their binary functions. Among them are the algebras with group reduct whose order is the product of at most 3 distinct primes. Title: A property of finite groups with abelian Sylow subgroups. Speaker: Matt Nickodemus Affiliation: CU Time: 4pm, Monday, November 6 Location: Math 220 Abstract: This will be the first of two talks in which I discuss extending Pontryagin's duality theorem for discrete abelian groups to finite nonabelian groups. In the second talk, I will show that we can extend Pontryagin's theorem to finite groups which have the property that all of their Sylow subgroups are abelian. We call such groups A-groups. Quackenbush and Szabo have shown that Pontryagin's duality theorem cannot be extended to finite groups which have a nonabelian Sylow subgroup. In this talk, I will discuss a property of A-groups which we will use in extending Pontryagin's duality theorem. Title: A division theorem for the free left distributive algebra with many generators. Speaker: Sheila Miller Affiliation: CU Time: 3pm, Monday, November 13 Location: Math 220 Abstract: The left distributive algebras (algebras satisfying the LD-law ) which occur in classical math are idempotent, hence not free. The free left distributive algebra $\mathcal{A}_1 = \mathcal{A}$ on one generator is representable as the span of an elementary embedding $j: V_{\lambda} \rightarrow V_{\lambda}$ (Laver) and is a subset of the braid group under a certain operation (Dehornoy). We will present a division theorem for the elements of $\mathcal{A}_{\kappa}$ . The algorithm, improving one of Laver for the one generator case, takes place not in $\mathcal{A}_{\kappa}$ but in $\mathcal{P}_{\kappa}$ --the result of enlarging $\mathcal{A}_{\kappa}$ to freely add a composition operation. Ways in which $\mathcal{A}$ --and more generally $\mathcal{A}_{\kappa}$ --are known or conjectured to be ``well-founded'' will be discussed. Title: A property of finite groups with abelian Sylow subgroups. Speaker: Nickodemus Affiliation: CU Time: 4pm, Monday, November 13 Location: Math 220 Abstract: Continuation from 11/06/06 Title: A proof of Moody's Conjecture. Speaker: Sheila Miller Affiliation: CU Time: 2pm, Thursday, November 16 Location: Math 220 Abstract: Moody's conjecture states: Given a, b, c, d $\in\mathcal{A}_{\kappa}$ such that ab = cd and a, b have no left divisors in common, likewise c, d, then a = c and b = d. We present a proof of Moody's conjecture using the division theorem for the elements of $P_{\kappa}$ established in the previous talk. Title: A property of finite groups with abelian Sylow subgroups. Speaker: Nickodemus Affiliation: CU Time: 3pm, Monday, November 16 Location: Math 220 Abstract: Continuation from 11/13/06 Title: Categorical equivalences between pseudovarieties. Speaker: Owen Lewis Affiliation: CU Time: 3pm, Monday, December 11 Location: Math 220 Abstract: TBA.
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