Universal Algebra and Logic

Spring 2010 Seminars

Time: Monday, 3 May 2010, 2 PM
Place: 1432 Stevenson Center
Speaker: Ralph McKenzie (Vanderbilt University)
Title: A term condition for omitting Types 1 and 2
Abstract: It has been known for some time that a locally finite variety’s omitting Tame Congruence types 1 and 2 is equivalent to having a pair of “special” weak near-unanimity operations of arities 3 and 4. In this talk we prove two further equivalent conditions, one of Taylor type and another relating to the absorption in a finite algebra in the variety. Time: Friday, 23 April 2010, 2 PM
Place: 1432 Stevenson Center
Speaker: Ralph McKenzie (Vanderbilt University)
Title: Barto’s proof of Zadori’s Conjecture II Time: Friday, 16 April 2010, 2 PM
Place: 1432 Stevenson Center
Speaker: Ralph McKenzie (Vanderbilt University)
Title: Barto’s proof of Zadori’s Conjecture
Abstract: I will present Libor Barto’s proof of Zadori’s Conjecture, that a finitely related algebra in a Jónnson variety has a near-unanimity operation. We will also discuss a strengthening of this conjuecture, due to Valeriote, which remains open. Time: Friday, 9 April 2010, 2 PM
Place: 1432 Stevenson Center
Speaker: TBA
Title: Constructing near unanimity operations from Jónnson operations
Abstract: We will discuss Libor Barto’s announced proof that a finite and finitely related algebra has a near-unanimity operation if it lies in a congruence-distributive variety, and hence its CSP problem is tractable. Time: Friday, 2 April 2010, 2 PM
Place: 1432 Stevenson Center
Speaker: Alex Wires (Vanderbilt University)
Title: Finitely Related Algebras with Cube-terms II
Time: Friday, 26 March 2010; 2 PM
Place: 1432 Stevenson Center
Speaker: Alex Wires (Vanderbilt University)
Title: Finitely Related Algebras with Cube-terms
Abstract: I will present recent results by Markovic, Maroti, and McKenzie strengthening the known connections between structural properties of an algebra, such as being finitely related or having a modular congruence lattice, and having special terms in its language. These results are advances in the pursuit of Valeriote’s conjecture that every finitely related finite algebra in a CM variety has a cube-term.

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Department of Mathematics
Vanderbilt University
Stevenson Center 1326
Nashville, TN 37240
U.S.A.

Phone: (615) 322-6672
Fax: (615) 343-0215