Nebraska alumna Kathryn Haymaker, an associate professor of mathematics at Villanova University, was a 2020 recipient of the prestigious Carl B. Allendoerfer Award from the Mathematical Association of America (MAA).
Haymaker and her research collaborator Beth Malmskog are one of two groups of collaborators who have been named as the recipients of the award, in recognition of their 2019 expository article, "What (Quilting) Circles Can Be Squared?" published in Mathematics Magazine.
"Our collaboration on the article began when Beth introduced me to a question that she had received from a non-mathematician friend. Beth had worked on the problem and created a blog post on her partial results, and then we collaborated to expand on what she had already done," said Haymaker, who started teaching at Villanova at the same time as Malmskog, in Fall 2014.
The findings of the article are that for a round-robin quilt exchange, it is possible to arrange the exchange so that every quilter visits every other when the number of quilters is composite—for example, for 4 or 15 people, Haymaker explained. When the number of quilters is prime, for small cases, it cannot be done. However, the feasibility for a prime number of quilters is unknown for numbers higher than 11. The quilting exchanges can be modeled as objects called row-complete Latin squares, and the article illustrates this connection, along with other results.
Another area of interest for both Haymaker and Malmskog is an outreach opportunity that started with the State Correctional Institute (SCI) Graterford, now SCI Phoenix. Together they started a monthly Math Circle in 2016, in which they worked with students and alumni of the Villanova program at Graterford (a college degree program that started in 1972).
Following Malmskog's move to Colorado College in 2017, Haymaker is still involved with the Math Circle, sending math packets by mail in 2020 due to the restrictions imposed due to COVID-19, and in the spring of 2021, she will be teaching a correspondence course there.
Teaching is a passion for Haymaker, which she discovered while working as a math tutor as an undergraduate. Currently teaching Mathematical Communities and Calculus II at Villanova, Haymaker said she enjoys working with students of all levels, especially undergraduates just starting out in the program and graduate students pursuing work on their master's capstone research.
Haymaker, who graduated from the UNL Department of Mathematics with her Ph.D. in May 2014, was able to collaborate on a research project in 2017 with current research assistant Sally (Robertson) Ahrens in the UNL Center for Science, Mathematics and Computer Education, when Ahrens was a master's student at Villanova. The Enumerating Tilings project resulted in the 2017 publication, "Counting Colorful Tilings of Rectangular Arrays," in the Journal of Integer Sequences.
"Sally and I collaborated to find a recursion for the number of ways to tile certain types of rectangles with squares, dominoes, and trominoes," Haymaker recalled. "The tilings portion was a new area for me to work on, so I want to credit Sally with being a wonderful collaborator and for working diligently to make that project a success."
Looking back at her time as a graduate student at Nebraska, Haymaker has fond memories of what led her to the program.
"I had heard from my undergraduate professors that UNL had a reputation as a supportive graduate program, and so I applied. At the time I was really interested in algebra and that was another feature that drew me to UNL," Haymaker said. "I was thrilled to be offered a spot in the program. I did find a lot of support from the department during my grad school years, from my advisor Dr. Christine Kelley, and from all of the professors and staff I had the opportunity to work with."
Even before Kelley officially advised Haymaker, Kelley brought Haymaker to a research conference early on, and Haymaker found Kelley's area of research to be an ideal mix of pure math ideas, with applications.
"Katie and I started working together soon after we both arrived at UNL, and we navigated the process together. I was fortunate to start out with such a strong student," Kelley said. "She was always up for my suggestions, like meeting on the weekend to read a huge a stack of papers! Along with sharing ideas, we shared many laughs, something we continue to this day."
Since graduation, Haymaker has had the opportunity to work with Kelley on writing papers, including one in 2019 in which they both collaborated with fellow Nebraska alumna Allison Beemer. The topic overlapped all of their interests, in a paper called "Absorbing sets of codes from finite geometries," which appeared in Cryptography and Communications.
Juggling her current research and teaching responsibilities, Haymaker was candid about the difficulties: "Having increased childcare needs for my toddler during COVID-19 has effectively halted my research progress at the moment, and I am far from the only parent in this position. It is a national problem. I hope that the situation gets better soon, but these are systemic issues."
Looking forward, Haymaker hopes to get back to a practice that blends her interests in both teaching and research.
"I have found that being able to incorporate research into my teaching when possible helps me to keep both fires going, so to speak. For example, the last time I taught the graduate capstone seminar, it sparked a research collaboration with a graduate student that ended up being a yearlong project. I have also done a few independent studies with students that helped me to maintain some research momentum," Haymaker said. "Villanova has been supportive with opportunities, such as the summer grant, a grant-writing workshop, and travel support. My department colleagues at Villanova are truly wonderful."
– Stephanie Vendetti