Logic Seminar Abstracts |
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Title: There are no infinite order polynomially complete lattices Speaker: Keith Kearnes Affiliation: CU Time: 3pm, Monday, September 22 Location: Math 220 Abstract: A lattice Lis order polynomially complete (OPC) if every monotone operation on L equals a polynomial operation. While there are many finite OPC lattices, Martin Goldstern and Saharon Shelah have recently shown that there are no infinite ones. I will present their proof. Title: There are no infinite order polynomially complete lattices Speaker: Kearnes Affiliation: CU Time: 3pm, Monday, September 29 Location: Math 220 Abstract: A continuation of the previous talk. Title: There are no infinite order polynomially complete lattices Speaker: Kearnes Affiliation: CU Time: 3pm, Monday, October 6 Location: Math 220 Abstract: A continuation of the previous talk. Title: There are no infinite order polynomially complete lattices Speaker: Kearnes Affiliation: CU Time: 3pm, Monday, October 13 Location: Math 220 Abstract: A continuation of the previous talk. Title: On rank functions for heaps Speaker: Richard Green Affiliation: CU Time: 3pm, Monday, October 20 Location: Math 220 Abstract: "Heaps of pieces" are certain isomorphism classes of labeled posets that have applications to statistical mechanics, algebraic combinatorics and theoretical computer science. I will present a simple and sufficient "local" criterion for a heap to be ranked as a partially ordered set. The talk will be elementary. Title: A division algorithm Speaker: Fred Richman Affiliation: Florida Atlantic University Time: 3pm, Monday, October 27 Location: Math 220 Abstract: A divisibility test of Arend Heyting for polynomials in one variable over a field, in an intuitionistic setting, may be thought of as a kind of division algorithm. It turns out that such a division algorithm holds for divisibility by polynomials of content 1 over any commutative ring in which nilpotent elements are zero. In this talk I will explain the intuitionistic background to the theorem and how it led to a piece of classical algebra. The (constructive) proof will not be included. Title: Congruence identities Speaker: Keith Kearnes Affiliation: CU Time: 3pm, Monday, November 17 Location: Math 220 Abstract: In 1900, Richard Dedekind showed that the ideal lattice of a ring is modular. That is, he showed that the modular law is a "congruence identity" for the class of rings. In this talk we will identify which equationally defined classes of algebras satisfy nontrivial congruence identities, and what the significance of this property is. Title: The Halpern-Läuchli partition theorem on products of perfect trees Speaker: Rich Laver Affiliation: CU Time: 3pm, Monday, November 24 Location: Math 220 Abstract: Title: Schubert varieties and free braidedness Speaker: Richard Green Affiliation: CU Time: 3pm, Monday, December 1 Location: Math 220 Abstract: I will present a necessary and sufficient combinatorial condition for a Schubert variety Xw to be smooth in the case where w is a freely braided element. This generalizes work of C.K. Fan on the corresponding problem for fully commutative elements. The problem of enumerating those freely braided elements w for which Xw is smooth can be solved nicely (in the most interesting cases) by using generating functions, from which explicit formulae can be derived. This is joint work with Jozsef Losonczy (LIU). |
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