Eric Zenk's Research page

Local Contact Information

Office: 1420

Telephone: 343-6137

Email: Eric.Zenk@Vanderbilt.edu

Biographic Information

Eric Zenk was born in 1977. He recieved a B.A. from St. John's University/College of St. Benedicts (MN) in 1999; he majored in mathematics and physics. Eric spent August 1999-August 2004 in graduate school at the University of Florida. Eric was awarded a Doctor of Philosophy degree (in mathematics) in August 2004. During the summers 1995-1999 he worked as a secretary, factory worker, and computer programmer. While in graduate school, Eric taught undergraduate mathematics classes (Precalculus, Calculus 1,2 and 3, Calculus for business majors 2, Mathematics for Prospective El. Ed. teachers). Eric's nonprofessional interests are: Molly Lemmer, singing, playing guitar, listening to classical music, bowling. He now works at Vanderbilt as an assistant professor, teaching Calculus 150B and pursuing research.

I actively participate in the <a href="http://www.math.vanderbilt.edu/~ua/">Universal Algebra and Logic Seminar</A>

Current Activities

I will be at Vanderbilt for the 2004-2005 and 2005-2006 school years. I expect my research time to be devoted to

• Learning about residuated structures,
• Learning about Universal Algebra,
• Continuing my work with Jorge Martinez.  (see below).

Current Projects

On Monoreflections of Tychonoff Locales. with JAMES. J. MADDEN. 

The Jonsson-Kieffer Property.  with KIRA ADARICHEVA, MIKLOS MAROTI, RALPH MCKENZIE, and J. B. NATION.  Examines when then meet of meet-prime elements in an algebraic lattice is 0.

My dissertation

"Subset Systems and Generalized Distributive Lattices" discusses/classifies some monads of the completely distributive lattice monad.  In order to do this, some machinery for dealing with subfunctors (i.e., natural transformations with each component extremal mono).  In addition, some discussion of spatial generalized distributive lattices is given.  Links to the full text are below.

Categories of Partial Frames a paper elaborating on some dissertation results has been accepted for publication by algebra universalis.  A link to the document -- here called catPfrm.pdf -- is below.

Collaboration with  Jorge Martinez.

Full text to each paper is avialable at Dr Martinez' webpage.

When an algebgraic frame is regular published in Algebra Universalis. This paper gives a characterization of when an algebraic frame is regular. Also, we discuss inductive nuclei on algebraic frames -- developing several `canonical' nuclei and showing that the class of inductive nuclei is a subframe of the frame of all nuclei. Applications to ordered algebra are given.

Dimension in Algebraic Frames, II submitted. We characterize the compact Hausdorff spaces X, for which the z-dimension is finite: the compact scattered spaces with finite Cantor-Bendixon index. The dimension is one less than the CB index.

Yosida Frames submitted. A Yosida frame is a frame in which each compact element is a meet of maximal elements. Yosida frames occur naturally when studying convex ell subgroups of C(X) and several other classes of lattice ordered groups.

Nuclear Typings of Frames vs Spatial Selectors.  In progress.

Text of my CV is given below.