# Annemily Hoganson ’24 receives prestigious Goldwater Scholarship

Hoganson studies mathematics at Carleton.

Mathematics major Annemily Hoganson ’24 joined just 412 other American undergraduate sophomores and juniors this year in receiving the Goldwater Scholarship for outstanding academic achievements in science, technology, engineering and mathematics (STEM).

The United States Congress established the scholarship in 1986 in honor of then-senator Barry Goldwater. Its purpose is to support future scientists, mathematicians and engineers by awarding up to $7,500 to students who have demonstrated exceptional achievement in STEM fields. A college may only nominate up to four students and this year saw over 5,000 candidates from 427 schools, making the scholarship one of the nation’s most prestigious.

Along with a series of short, career-focused questions, the centerpiece of the Goldwater Scholarship’s application process is a research essay based on the applicant’s previous work. Hoganson wrote about her experience participating in an REU (Research Experience for Undergraduates) at the University of Virginia (UVA) in the summer of 2022.

At UVA, Hoganson worked with graduate student Thomas Jaklitsch and Professor Ken Ono to conduct research on partition functions. In number theory, the branch of mathematics concerned with integers and prime numbers, a partition is a way of writing an integer as a sum (for instance, one partition of 3 is 2+1). Number theorists can study partitions through partition functions, mathematical formulas counting how many partitions an integer has. Partition functions are also frequently used in statistical mechanics, particle physics and many other areas of mathematics.

Hoganson and Jaklitsch ultimately produced the paper, “On certain McKay numbers of symmetric groups,” which was published in the peer-reviewed mathematics publication The Ramanujan Journal on Jan. 30, 2023.

“We started out the program by doing some background reading,” Hoganson said, “and then came up with conjectures about the functions we were interested in.”

From there, it was a matter of “working to prove” the conjectures.

“I proved some divisibility properties of partition functions,” she said. “We were looking at some functions that count specific types of partitions, and we proved that, asymptotically, one hundred percent of these functions are divisible by any integer,” thereby answering a question Ono had previously posed.

Hoganson hopes to continue her research long after her time at Carleton.

“I’m particularly interested in number theory,” she said, and, after studying mathematics in graduate school, plans to “hopefully someday become a professor and do research and teaching.”

The scholarship will support her in this goal by helping finance her final year at Carleton and introducing her to a community of other like-minded mathematicians in the form of the other scholarship recipients.

“I feel really honored to have been selected,” Hoganson said.

Hoganson will be spending this summer participating in the Undergraduate Research Program at the Fields Institute for Research in Mathematical Science, which will focus once again on number theory. She is also a former member of the women’s swimming and diving team at Carleton.

“I’m really grateful for the support of the entire math department here at Carleton, especially my adviser [Assistant Professor of Mathematics] Caroline Turnage-Butterbaugh,” Hoganson said. She also thanks her research mentor Ono.

The Goldwater Scholarship application and nomination process is managed by Carleton’s Office of Student Fellowships.