# Fall 2011 Seminars

 Time: Friday, 9 December 2011, 4:10 PM Place: SC 1310 Speaker: Simone Bova Title: Classifying Unification over Involutive Lattices by Unification Type  Involutive lattices are distributive lattices with an involution satisfying De Morgan laws; for instance, Boolean algebras are complemented involutive lattices. For a fixed algebraic variety, (equational) unification is the problem of solving equations in the context of free algebras. The solutions to a particular instance of the unification problem are ordered by generality in a natural way. Algorithmically, the instance is nice or bad depending on whether or not the set of all solutions admits a subset of finitely many pairwise incomparable most general solutions, and the type of an instance (nullary, unary, finitary, or infinitary) includes this information. By reducing the classification to the classification of a suitable class of finite posets, we classify all instances of the unification problem over involutive lattices with respect to their types. Time: Friday, 18 November 2011, 4:10 PM Place: SC 1310 Speaker: Marcin Kozik Title: Time: Friday, 11 November 2011, 4:10 PM Place: SC 1310 Speaker: William Young Title: On Cone Algebras Time: Friday, 28 October 2011, 4:10 PM Place: SC 1310 Speaker: Olga Sapir Title: How to recognize finitely based words among words in at most two non-linear letters  An algebra is said to be finitely based if there is a finite subset of its identities from which all of its identities may be deduced. Let $A$ be an alphabet and $W$ be a set of words in a free monoid $A*$. Let $S(W)$ denote the Rees quotient over the ideal of $A*$ consisting of all words that are not subwords of words in $W$. We call a set of words $W$ finitely based if the monoid $S(W)$ is finitely based. A letter $x$ in a word $u$ is called linear if $x$ occurs once in $u$, otherwise $x$ is called non-linear. We find a simple algorithm that recognizes finitely based words among the words in at most two non-linear letters. Time: Friday, 21 October 2011, 4:10 PM Place: SC 1310 Speaker: Ralph McKenzie Title: Directly Representable Varieities Time: Friday, 30 September 2011, 4:10 PM Place: SC 1310 Speaker: Simone Bova (Vanderbilt University) Title: The Finite Homomorphism Preservation Theorem  Reading Group: Rossman, B, “Homorphism Preservation Theorems”, Journal of the ACM, July 2008 Time: Friday, 23 September 2011, 4:10 PM Place: SC 1310 Speaker: Ralph McKenzie (Vanderbilt University) Title: The Finite Homomorphism Preservation Theorem  Reading Group: Rossman, B, “Homorphism Preservation Theorems”, Journal of the ACM, July 2008 Time: Friday, 16 September 2011, 4:10 PM Place: SC 1310 Speaker: Matthew Smedberg (Vanderbilt University) Title: The Finite Homomorphism Preservation Theorem  Reading Group: Rossman, B, “Homorphism Preservation Theorems”, Journal of the ACM, July 2008

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

Phone: (615) 322-6672
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