Universal Algebra and Logic

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

Back Home   

Contact Information

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

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