About Me

I am an Assistant Professor of the Practice in the Mathematics Department and the Director of the ASCEND program, which is the summer online program for the incoming first years. I works primarily in digital resource development and mathematical pedagogy. In the past few years, I helped create both the Summer Online Calculus III and Introduction to Linear Algebra and Differential Equations courses. I frequently implement digital materials and alternative teaching practices and plans to further research the impact of these non-traditional teaching methodologies to enhance student learning.

As a mission hire with the deNicola Center for Ethics and Culture, I work to support the Catholic mission of the University through my research and teaching. I hope my research in pedagogy can be used to address injustice and create an environment where all students can thrive. Before teaching any class, I reflect on the words of Blessed Basil Moreau, "the mind will not be cultivated at the expense of the heart."

My mathematical research interest is in the mathematics of quantum mechanics. I specifically looks at Segal-Bargmann Space and relationships with the different types of Segal-Bargmann transforms.

Below is an adapted version of my dissertation's abstract.

In Real Euclidean Space, polar coordinates allow mathematicians to calculate the norm of higher dimensional SO-invariant functions with relative ease by reducing the problem to a 1-dimensional integral. In this dissertation I look at the Complex Segal--Bargmann Space using the C transform. I find there is a "holomorphic" version of polar coordinates that allows us to do the same in the odd dimensional cases. A geometric approach for this was done by Areerak Kaewthep and Wicharn Lewkeeratiyutkul using the B transform, but this method is not easily generalized to non-Euclidean Spaces. Motivated by the works of Gestur Olafsson and Henrik Schlichtkrull, I use shift operators to find this "holomorphic" version of polar coordinates in C version of the Segal--Bargmann transform.

Previously I have presented an exposition of the work by Thomas and Villegas-Blas, titled Asymptotics of Rydberg States for the Hydrogen Atom

Asymptotics of Rydberg States

Additional I wish to advance the understand of undergraduate mathematics education. I work with a variety of different professors to establish different methods of teaching and compare the effectiveness of these methods.