Esther Banaian's Homepage

Contact Info

Office: Vincent Hall 550
About me: I am a third year graduate student at the University of Minnesota. My advisor is Gregg Musiker. I did my undergrad at the College of Saint Benedict.
When I am not doing math, I enjoy running, lifting, petting dogs and cats, and playing cribbage. I run with the Collegeville Running Club . If you are interested in joining us for a run, please let me know!


This academic year (2018-2019) I am co-organizing the Student Combinatorics and Algebra Seminar with Sarah Brauner . If you would like to speak at this seminar, feel free to speak with either of us.

Work with Undergraduate

Research and Readings I have read about number theory and representation theory with several undergraduate students. I am open to reading about a wide range of topics.
As for research, I have worked on projects in enumerative combinatorics (juggling patterns), algebraic combinatorics (cluster algebras), and often something inbetween (frieze patterns, snake graphs). This has been both through the combinatorics REU at UMN and, less formally, through semester long experiences.
Students do not need a large amount of background to work on or read about some of these topics. Please contact me if you would be interested in devling into higher math with me!
Mathematics Project at Minnesota I am an organizer for the Mathematics Project at Minnesota (MPM). This is an annual four-day workshop designed to provide mentorship, professional develoment, and community building for students from underrepresented groups who are interested in mathematics.

My Own Research

I am very interested in cluster algebras and quiver representations. I am currently looking to mirror the correspondence between frieze patterns and cluster algebras to include certain frieze patterns of algebraic integers and certain families of generalized cluster algebras. Before coming to graduate school, I spent a lot of time investigating the mathematics of juggling. This topic still holds a special place in my heart, and I still have unanswered questions I would love to work on.