Research Portfolio

what I have done and what I am interested in

This page shows my current research interests as well as some of my past publications in each area. My research interests are diverse, and I am always open to thinking about mathematical problems in new areas.

Minimal free resolutions and Betti numbers of monomial ideals

Throughout my academic career, and starting in graduate school, I have been interested in the behavior of monomial ideals arising from combinatorial objects. In particular, I am interested in studying how the combinatorics of the objects relate to the behavior of the minimal free resolutions of the corresponding monomial ideals. I have studied path ideals, whose monomial generators correspond to paths of a fixed length in a graph; and I have studied domino ideals, whose monomial generators correspond to domino tilings of a rectangle. Here are some of my past publications in the area of monomial ideals:

Mathematical modeling

In the summer of 2015, I was selected to participate in the Research Experiences for Undergraduate Faculty (REUF) program sponsored by the American Institute of Mathematics and the National Science Foundation in Providence, RI. At this workshop I was introduced to the area of mathematical modeling, specifically relating to disease epidemiology. My research group modeled medication distribution for Onchocerciasis, also known as River Blindess, in sub-Saharan Africa. Here is my only publication in the area of math modeling:

Mathematics and the fiber arts

One of my hobbies is knitting, and I have been working to design patterns that are based on mathematical ideas. I designed a double knit scarf that is based on both the dragon fractal and the Fibonacci sequence of numbers. The finished product was accepted into the Exhibition of Mathematical Art at the 2016 Joint Mathematics Meetings in Seattle, Washington. Here is the information for that art exhibition:

  • Rachelle Bouchat, Dragon curve double knit scarf , 2016 Joint Mathematics Meetings Exhibition of Mathematical Art, Tessellations Publishing (ISBN 978-1-938664-17-5)

To find out even more, here is my CV:

bouchat_cv.pdf