About Me

I am a commutative algebraist from Severn, Maryland. My graduate degree is from Cornell University in 2011, and my undergraduate degree is from St. Mary's College of Maryland in 2004.

I am also a recent Project NExT Fellow (Silver Dot, 2012-2013) and a Section NExT Fellow for the MD-DC-VA section(2011-2012).

View from Inlet Island

Primary Research Interests

My research primarily focused on computing the projective dimension, regularity, and Betti numbers of ideals over polynomial rings and residue fields over quotient rings. In particular, my thesis results were focused on:

My current research has moved into producing explicit resolutions of residue fields \(\Bbbk\) over quotient rings \(S=\Bbbk[x_1,..,x_n]/M\), where \(M=(m_1,..,m_r)\) is a monomial ideal. This extends results of Berglund, Blasiak and Hersh on the Poincaré series of such rings \(S\).

Undergraduate Teaching and Research

Hood College 2011-present

Undergraduate Research Group

Currently, I have Alison Schuetz (a senior mathematics major at Hood College) working on a project on combinatorial games. In particular, she has been focusing on games arising in combinatorial topology and algebra.

Last summer, I had two undergraduate research students (Brian Penko '15 and Megan Rodriguez '15) working on a project in Buchberger Graphs of Trivariate Monomial Ideals. Our focus is on enumerating minimal (strongly generic) monomial ideals with a Buchberger graph realizing a fixed planar graph, and providing minimal bounds on degrees of generators for such ideals.

In Summer 2012, I had two undergraduate research students working on a project on the Combinatorics of the Mandelbrot Set. In particular, they focused on identifying points in the Mandelbrot set with orbit patterns corresponding to \(H\)-compositions of numbers \(n\in{\mathbb N}\), classifying and counting points \(x\in{\mathbb R}\) with period \(n\) by their combinatorial type, and producing explicit coefficients of infinitely iterated Multibrot polynomials.

Our paper from that summer research has been submitted, and both students attended MathFest 2012 in Madison, WI to present their work.


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