Research Portfolio

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:

• Rachelle Bouchat and Tricia Brown, Multigraded Betti numbers of Möbius domino ideals, Communications in Algebra 50(5) (2021), 2269--2278.

• Rachelle Bouchat and Tricia Brown, Fibonacci numbers and resolutions of domino ideals , J. Algebra Comb. Discrete Struct. Appl. 6(2) (2019), 63-74.

• Rachelle Bouchat and Tricia Brown, Minimal free resolutions of 2xn domino tilings , J. Algebra Appl. 18(6) (2019), art. id. 1950118 (16 pages).

• Rachelle Bouchat and Tricia Brown, A constructive approach to minimal free resolutions of path ideals of trees , J. Algebra comb. Discrete Struct. Appl. 4(1) (2017), 1-13.

• Rachelle Bouchat and Tricia Brown, Multi-graded Betti numbers of path ideals of trees , J. Algebra Appl. 16(1) (2017), 1-20.

• Rachelle Bouchat, Augustine O'Keefe, and Huy Tai Ha, Path ideals of rooted trees and their graded Betti numbers , Journal of Combinatorial Theory, Series A, 118 (2011), 2411-2425.

• Rachelle Bouchat, Free resolutions of some edge ideals of simple graphs , J. Commut. Algebra, 2(1) (2010), 1-36.

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:

• Glenn Ledder, Donna Sylvester, Rachelle Bouchat, and Johann Thiel, Continuous and pulsed epidemiological models for onchocerciasis with implications for eradication strategy , Mathematical Biosciences and Engineering 15(4) (2018), 841-862.

Scholarship of teaching and learning

I have always been interested in innovation inside and outside the classroom that helps make mathematics more accessible and inclusive to students and the general population. I have just recently started publishing my activities for the classroom and articles for a general audience.

• Rachelle Bouchat and Kristen Barnard, "Using mathematical modeling to motivate polynomial end-behavior," Ohio J. School Math. 91(1), 10-16.

• Rachelle Bouchat, "Review of `Humble Pi: When Math Goes Wrong in the Real World," Math Horizons 29(2) (2022).

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: