Brian Taylor 


permanent email: brian_david_taylor@alum.mit.edu
old email: bdt@math.wayne.edu 
http://www.math.wayne.edu/~bdt  (the page you're looking at is temporary)

Mailing Address:
Brian Taylor
c/o Department of Mathematics (please forward)
Wayne State University 
Detroit, Michigan 48202
USA
 

My research interests include combinatorics (including umbral calculus), representation theory, and symbolic computation, and the relationships between these fields.
 
   

My mathematical genealogy

My thesis advisor, Gian-Carlo Rota, passed away on April 18, 1999. One of my mathematical siblings keeps part of our mutual mathematical family tree. Shortly after his death, I wrote down some remembrances of my advisor. They were collected with the thoughts of numerous other students and colleagues by the SIAM newsletter on Discrete Mathematics.

Research Overview

Determinants, Representation Theory, and Symbolic Computation

Combinatorics, among many other things, involves the study of (partially) ordered structures, and some of my favorite questions center on understanding what happens when one takes an algebraic structure and imposes a "compatible" order. A relatively familiar example of this situation is Groebner basis theory in which an ideal in a polynomial ring may be studied (both theoretically and computationally) via the imposition of a total order on the monomials in the ring. My research in this area uses Straightening Laws and other variants of the above techniques to study representations of the general linear group corresponding to "row-convex diagrams." A brief (11 pages) but fairly readable introduction to this material may be found in my FPSAC '97 abstract "Straightening laws for row-convex tableaux," also available in a postscript and DVI.

List of papers/preprints related to this field
Note: The files here are not definitive, but I've included pointers to the final article. Note that in general the publisher of the relevant journal retains copyright of the article once published.

Umbral Calculus

Another useful technique in algebraic combinatorics involves the imposition of an algebraic structure on a combinatorial problem. A very particular example of this is the umbral calculus in which complicated identities in a vector space, V, are derived by working in a polynomial ring which projects down onto V. My publications in the area appear below (in preprint format).
Again, the files here are not definitive, but I've included pointers to the final article. Note that in general the publisher of the relevant journal retains copyright of the article once published.

Miscellaneous paper

This one doesn't fit into the above categories. It's still fun though.

Special Session on Algebraic Combinatorics

I've preserved some links to the special session on Algebraic Combinatorics that Tricia Hersh and I organized for the AMS sectional meeting in Ann Arbor, March 1-3, 2002.  

 

Brian D. Taylor