Research

Research Interests

I have been working on developing my skills with various commutative algebra and algebraic geometry tools such as symbolic powers of ideals, Gröbner bases, and sheaf theory. I hope to use these tools to solve problems in areas such as mathematical neuroscience and topological data analysis.

My current research questions include

What can be learned about a neural code by computing the multigraded Betti numbers of the corresponding polarized neural ideal via Hochster’s Formula?

Can we translate Hochster’s formula to compute Betti numbers by using combinatorial properties of the neural code?

What is the relationship between polarized neural ideals whose codes induce the same simplicial complex?

Seminars Attended

I am currently regularly attending the following seminars at University of Nebraska-Lincoln

Conferences/Workshops Attended