This page describes my mathematical interests, experiences and influences.
My area of research is geometric topology. My master's thesis presented new results on fibered links. I am currently working on 1.) knot, link and braid algorithms, 2.) applications of my master's thesis to open book decompositions of 3-manifolds, and 3.) other questions.
I am a junior researcher at Euclid Lab. David Gay is my research mentor (see below).
Teaching and Mentoring
I would drive an hour and a half twice a week out to the town of Sells in the Tohono O'odham Nation to mentor and tutor Baboquivari Jr./Sr. High School students participating in the University of Arizona's Academic Preparation for Excellence Program, an early outreach program for middle and high school students.
I was a teaching assistant for a mathematics enrichment summer program for incoming freshmen at Pueblo High School in Tucson, Arizona.
I was a math, science and computer science group tutor for the Math and Science Learning Center at the University of Arizona. I met with each group once a week throughout the semester and I helped students in the drop-in tutoring room.
In the summer of 2010, I was a junior mentor for Camp Euclid.
Every week he would meet with a group of his advisees for lunch at a nearby restaurant and help us with real analysis and abstract algebra.
Every couple of weeks I would go to his office to talk about my research project that he was directing. He had a petri dish full of flour populated with flour beetles in his office. We were modeling the population dynamics of flour beetles.David Gay
He helped me with my topology classes in graduate school. Later, I discussed mathematics with him regularly while doing my master's thesis research. Now, together, we have founded Euclid Lab, and he is my research mentor.
I am a co-founder of Euclid Lab, the deputy director of Euclid Lab, and also the vice-president and secretary of its Board of Directors.
I went to Horizon High School in Paradise Valley, Arizona, and graduated in 1988. I then went to the University of Arizona for college, where I graduated with a B.S. in mathematics in 1996. Afterwards, I went to the University of California, Berkeley for graduate school, where I graduated with an M.A. in mathematics in 2002.