# Juliette Benitez

## My Research

I study math, theoretical physics and philosophy. In math, I study foundations, logic, geometry and topology and number theory. My master's thesis in math presented new results in geometric topology - on fibered, surgery links. And, in philosophy, I study metaphysics and philosophy of logic, math, physics, science . . . .

But, in general, I'm curious about unsolved problems of all kinds.

I'm a junior researcher at Euclid Lab.

Here I describe a number of my activities, experiences, influences and background.

## Teaching

In my freshman and sophomore years of college, I drove an hour-and-a-half, twice-a-week, out to the town of Sells, in the Tohono O'odham Nation - I tutored math and science to Baboquivari Jr./Sr. High School students participating in the U of A's (University of Arizona's) Academic Preparation for Excellence Program (an early-outreach program). I was also their mentor.

In my junior and senior years, I tutored math, science and computer science groups for the Math and Science Learning Center, at the U of A. I met with each group, once-a-week, throughout the semester and helped students in the drop-in tutoring room.

In-between my junior and senior year, I assisted teachers at a math enrichment summer program for incoming, at-risk freshmen at Pueblo High School, in Tucson, Arizona. Fellow math majors and I presented a "hands-on" mini-workshop, to pairs of students, with our department's mobile math lab.

At Euclid Lab, in Athens, Georgia, I present unsolved problems to the general public, at all levels. As a junior mentor of the 4-Sphere (our hands-on research lab), I presented a number of unsolved problems at the 3rd and 4th USA Science and Engineering Festivals, at David C. Barrow Elementary School (for local elementary school students!), and at the Summer Math Camp (for junior and senior high school students) at Dine College, in the Navajo Nation.

I'm a mentor for Euclid Lab's research course (MATH 1: Research, including the Prime Numbers Lab) and the Flatland Institute (a research program for youth).

## Writing

I write for Euclid Lab's wiki, U N S O L V E D; I've writen a working draft of Euclid Lab's beginner's workbook on unsolved problems, Conundrums and Challenges; and I write about my research.

In my junior year of college, a fellow math major and I co-wrote a mini-math lab workbook for our department's math lab.

## Developing

I develop research kits, hands-on exhibits and multi-media featuring unsolved problems.

Organizing

I organize research days (e.g. Pythagoras Trek), research programs (e.g. Camp Euclid and the Flatland Institute) and workshops (e.g. the Workshop in Foundations and Philosophy of the Mathematical Sciences).

I'm the co-PI for an award from the AMS (American Mathematical Society) Epsilon Fund for Young Scholars Programs; a co-PI for a sub-award from the NSF (National Science Foundation) for Camp Euclid; and a PI for a Startup Allocation award to use the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by the NSF.

## My Background

In high school, I decided that I wanted to become a researcher, because I liked trying to solve challenging problems and I wanted to help the world by trying to solve the "mysteries" of the universe. I went to Horizon High School in Paradise Valley, Arizona (I graduated in 1988).

During the summer before my senior year, I helped, at the U of A, in a neurophysiology research lab which was studying motor neurons.

In my senior year, I took an independent study course in math with Mr. Jensen (John Jensen). I worked independently in the math department's office. He had assigned me to choose and read a math journal article and we met regularly to discuss it. He was one of my earliest mentors.

After I graduated, I went to the U of A for a bachelor's degree (I graduated in math in 1996).

During my freshman year, I helped in a chemical engineering research lab which was crystallizing gypsum.

During the first semester of my upper-division studies, my undergraduate advisor, Dr. Velez (Bill Velez), met for lunch, once-a-week, with a group of his advisees to help us with real analysis and abstract algebra. His advice, when I was a sophomore, had motivated my decision to major in math.

In my junior year, every couple of weeks, I went to Dr. Cushing's (Jim Cushing's) office to talk about my research project that he was directing. In his office, he had a petri dish full of flour - populated with flour beetles. We were modeling chaos in the population dynamics of flour beetles. He was my first mathematics research mentor.

In the summer of my junior year, I participated in the Geometry Center's Summer Institute for Undergraduates at the University of Minnesota. My project was to "visuallize" eigenfunctions of the hyperbolic Laplacian - I was mentored by Paul (Paul Burchard). My algorithm didn't terminate (at least during the program), but the math, itself, was beautiful.

I went to UC Berkeley for graduate school in math (I graduated with a master's degree in 2002).

In-between my studies, helping an inventor to develop a speech recognizer, I used math to model speech.

In school, my friend, Dave (David Gay), helped me with my topology classes; and, later, he "talked math" with me, while I was puzzling over the unsolved problem, "Do surgery links fiber 3-manifolds?". I solved it and, after I graduated, Dave and I created Euclid Lab - a mathematics research lab with "outreach to all" as a side mission.

Lately, I've participated in workshops in philosophy of physics, science, logic, language and information, metaphysics, fundamentality and grounding . . . . . . . .

In the next year (or so), I plan to begin doctoral study.

I'm a member of the American Mathematical Society, the Mathematical Association of America, the American Physical Society, the American Philosophical Society, the Philosophy of Science Association and the Society for Exact Philosophy.