Bernadette’s research is in the areas of algebraic geometry and commutative algebra. Under the guidance of her adviser, Dr. Juan Migliore, she investigates the shape of pure O-sequences, which are the Hilbert functions of level Artinian monomial algebras. Hillbert functions measure the dimension of these algebras in each degree; listing these values for all degrees produces a sequence of numbers.
Bernadette’s thesis concentrates on the unimodality of these sequences assuming certain additional properties. A sequence is unimodal if it does not increase after it has begun to decrease. Pure O-sequences have applications in other areas of math, including the study of error-correcting codes.
In addition to research, Bernadette appreciates the opportunity to connect with undergraduates and share her passion for mathematics through teaching—both as a teaching assistant for several courses and, more importantly, as the main instructor for Finite Mathematics, Calculus B, and Principles of Calculus.
She says: “Under the guidance of experienced professors within the math department, I have developed in my teaching ability and have grown to love teaching. It is very rewarding to work with students and watch as their understanding and appreciation for mathematics grows throughout the semester. This experience has been invaluable to me as I prepare to graduate and begin a career in academia.”
Bernadette is involved in the student group Catholic Graduate Community, where she spends time serving others, deepening her faith, and socializing with other graduate students. She also enjoys the opportunity to be a participant in intramurals sponsored by Rec Sports and town leagues while sharing in the ubiquitous school spirit for all of Notre Dame’s athletic teams.