# Allechar Serrano López: Math Grad Student

*The image above illustrates Serrano López's research. *

Allechar Serrano López enjoyed studying math when she was growing up, but she also had periods where she focused on other things. After she took a course in groups and rings as well as another in field theory, she decided to complete an undergraduate degree in math.

Before coming to the U to work on a Ph.D. in mathematics, Serrano López had earned bachelor’s degrees in mathematics and economics from the University of Costa Rica. She was also an instructor at the university and worked for the research department of the Central Bank of Costa Rica.

Her decision to come to Utah came down to a phone call from the Chair of the Mathematics Department, asking her if she would be willing to teach a full load of three sections instead of one. “I was in my cubicle at the Central Bank of Costa Rica, and I had two hours to decide,” said Serrano López. She made the jump and began teaching and working on a Ph.D. in 2015.

“Being in grad school is definitely a period of adjustment, and it can be especially challenging for an international student,” she said. “Not having a credit record in the U.S. makes it hard to rent an apartment or purchase basic necessities.”

**Number Theory Research**

Serrano López’s research focuses on number theory—the area of math that studies integers (and their generalizations) and their properties—and her work involves counting elliptic curves over quadratic fields with prescribed torsion points. “These torsion points form a set with a very specific structure, and there are only a few possibilities for this structure,” she said. She works under the direction of associate professor, Stefan Patrikis. “Stefan is very helpful and knowledgeable, and he also has built our research group from scratch,” said Serrano López.

A few years ago, she became interested in teaching math education.

“The system in the United States is very different from the one I grew up with, and experiencing how math is taught here has made me more aware of the lack of representation in STEM (Science Technology Engineering and Math),” she said. “Once you begin to notice you’re the only woman in the room or the only person of color, you can’t make it go away.” Serrano López is interested in mathematics education because she thinks everyone deserves to be math literate in order to make decisions about their lives and to process information, such as interpreting polls, taking out loans, and refinancing student debt, etc.

**STEM Research and Fellowship Project **

She is currently working on a fellowship project called “Building an Inclusive Math Learning Environment to Support Student Retention in STEM.” The project consists of workshops for instructors and discussions with undergraduate students to understand the current climate in the U’s Math Department.

“One of the first steps towards an inclusive classroom is convincing instructors that there’s an existing problem that needs to be addressed,” said Serrano López. “There has to be a commitment from the administration to make change happen, and I don’t think we’re there yet,” she said.

Serrano López praises the efforts of instructors Kelly MacArthur and Amanda Cangelosi in serving as teaching mentors. They have helped Serrano López learn the importance of providing solid instruction and the best ways to serve students. Serrano López is also part of a collective for women of color in academia at the University of Utah, organized by Annie Fukushima, assistant professor in the Division of Ethnic Studies with the School for Cultural & Social Transformation. “Annie and the other members of the group have been very welcoming, and I enjoy attending their social and professional development events,” she said.

**AWM and Latinos in Action **

It wasn’t until her third year as a graduate student that Serrano López got involved with Association for Women in Mathematics (AWM). She has found the chapter helpful in building a sense of community and in providing support to women grad students. “Being a member has brought me closer to people in different research areas, with whom I would never have interacted if it weren’t for AWM.”

Serrano López is also active in the U’s chapter for Latinos in Action (LIA), as well as the U’s Society for Advancement of Chicanos/Hispanics and Native Americans in Science (SACNAS). She thinks these organizations are valuable in providing role models and helping underrepresented groups realize opportunities. “Often students from underrepresented groups don’t see themselves when they think of a mathematician, so it doesn’t occur to them to pursue a career in mathematics,” she said.

**Life Away from Math **

When she isn’t teaching or doing research, she loves to bake and make desserts. She is well-known for her homemade ice cream, and she also bakes bread. She likes to read and tries to read at least one book in Spanish every summer.

Serrano López hopes to remain in the U.S. and plans to apply for postdoc positions. Ultimately, she’d like to become a professor at a liberal arts college.