Monroe Stephenson

Intro

Currently, I am a visitor to the MPI MiS in Leipzig working under Bernd Sturmfels on a Fulbright Scholarship. In May 2023, I graduated from Reed College with a BA in Mathematics.

My CV is here.

Research

In the summer of 2022, I participated in an REU at the Hebrew University, where I worked under Karim Adiprasito, funded by his ERC Consolidator grant. We studied the Hopf Conjecture initially, but then we discovered a generalization and simplification of Karim's proof of the g-conjecture. Specifically, our approach involves embedding the simplicial complex into the moment curve. Our draft will soon be on the arXiv.

In the summer of 2021, I participated in an REU at the University of Michigan, where I worked under Jennifer Kenkel, Janet Page, and Daniel Smolkin funded by Karen Smith’s NSF grant DMS-1801697. We studied the differential power operation on ideals. We began with a focus on monomial ideals in characteristic 0 and found a class of ideals whose differential powers are eventually principal. We also studied the containment problem between ordinary and differential powers of ideals in analogy to earlier work comparing ordinary and symbolic powers of ideals. We further defined a possible closure operation on ideals, called differential closure, in analogy with integral and tight closure. We showed that this closure operation agrees with taking the radical of an ideal if and only if the ambient ring is a simple D-module. Our pre-print is here.

In the summer of 2020, I participated in an REU at PSU by PI Christof Teuscher. The REU is called an altREU because Christof created it considering the COVID-19 Pandemic. Christof recognized that many would lose the opportunity to research during the summer, with his own NSF REU site being canceled. I had been working with Art Duval of UTEP on the Abelian Sandpile Model applied to DDoS mitigation. Our final writeup can be found here.

In the summer of 2019, I worked under Andrew Whitbeck within the Experimental High-Energy Particle department at TTU, working toward developing the LDMX project. Lab work included SketchUp design, data collection from oscilloscopes, scintillators, and PMTs, data science with Python, and electrical circuit design and modification. My final writeup can be found here.

About

Contact

Elements

i = 0;

while (!deck.isInOrder()) {
    print 'Iteration ' + i;
    deck.shuffle();
    i++;
}

print 'It took ' + i + ' iterations to sort the deck.';