Student Essay Contest

Shelly Harvey: Knot your typical California Girl!

2012 AWM Essay Contest: High School Honorable Mention

by Anita Rao

If you build it, they will come!

Spending your summer studying abstract mathematics may not seem like fun for most people. However, for me participating in a two week enrichment program in Houston with twenty gifted girls was a dream come true. The Rice University Mathematical Institute for Young Women is the brainchild of Dr. Shelly Harvey, and she uses it to introduce rising 9th and 10th grade women to abstract mathematics through knot theory and its applications. This outreach program funded by a National Science Foundation CAREER grant is just one example of the many different ways Dr. Harvey is changing the world around her.

Despite her relative youth, Dr. Shelly Harvey has already achieved a great deal. She is a researcher who has solved decades-old open problems, an inspiring and engaging teacher, a mentor for graduate students, and a role model for aspiring mathematicians.

Shelly Harvey’s journey began in Rancho Cucamonga, a suburb of Los Angeles, California. Her father was a high school math teacher and her mother a hair dresser. Though only her father and uncle had gone to college in her family, education was stressed and her parents encouraged her to excel. As a child she always strived to be the best, and found herself to be healthily competitive. She loved puzzles and mind twisters, and participated in school sports such as volleyball and track. However, she was not your typical California Girl!

After graduating from Etiwanda High School, Shelly was admitted to Cal Poly in San Luis Obispo to study Industrial Engineering. In her sophomore year, she came to the realization that mathematics was not just “about plugging and chugging”, but rather it entailed understanding the foundations of the subject. One of her professors suggested she pursue a summer program called Research Experience for Undergraduates (REU). She was accepted to the program at Louisiana State University in Baton Rouge, where she met many like-minded students and studied a branch of topology called knot theory. She learned to give talks, and present her research work in weekly meetings. She came away from the experience understanding the challenges of research and with the fire in her belly to pursue graduate school.

Still an undergraduate, Shelly was inspired to attend an REU the following summer at Cornell University. Investigating different areas of convex geometry led to her first paper “The Voronoi Vectors of a Lattice” which was presented at the MathFest in Seattle.

Subsequently, she attended Rice University where she studied under Prof. Tim Cochran. Her doctoral thesis entitled “Higher-order polynomial invariants of 3-manifolds giving lower bounds for the Thurston norm” extended the Alexander polynomial for links and general three manifolds. After receiving her doctorate in 2002, Dr. Harvey was awarded the NSF Mathematical Science Postdoctoral Fellowship which she spent first at UC San Diego, followed by two years at the Massachusetts Institute of Technology, in Cambridge, MA.

The theory of knots had become an exciting field of mathematics, and Shelly Harvey was in the midst of it. Scientists and mathematicians were encountering knots in a variety of areas such as string theory in Physics, statistical mechanics, molecular chemistry and DNA strand untangling. One of the fundamental goals in knot theory is to find a method to determine if different-looking knots are equivalent. Over a hundred years ago, the French mathematician Henri Poincaré introduced the concept of “the fundamental group of a knot” and developed an algebraic metric to measure all possible paths that can be navigated in the space surrounding a knot. Dr. Harvey’s insight was in realizing that the “fundamental group of the knot” had an underlying algebraic structure where some paths were more robust than others. In a paper published in the journal Geometry & Topology, Dr. Harvey showed that this algebraic structure remained unchanged even in four dimensions even as the knots were unraveled.

In 2005, Dr. Shelly Harvey joined the mathematics department at Rice University as its first female tenure-track faculty member. Presently an Associate Professor, she has supervised several PhD students and post-doctoral fellows. Her area of interest is in low-dimensional topology where she continues to produce exciting results. Her career allows her to travel around the world and interact with the leading researchers in her areas of interest. In her spare time, she is passionate about music, and collects headphones.

Dr. Harvey is not only on the cutting edge in her academic field, but also endeavors to make her subject accessible to the larger society. Her service to the community involves organizing workshops and making presentations to students and teachers in middle schools and high schools. With many role models like herself for women today, she is confident that in the future there will be even more representation of women in careers involving mathematics.

About the Student:

Currently a sophomore at Glenda Dawson High School, I will be transferring to the residential Texas Academy of Mathematics and Science in Denton, TX for my final two years of high school. I have participated in science fairs since I was in 7th grade. This year, my math project “Lorenz and Modular Flows are Knot Similar” won first place at the ExxonMobil Texas Science and Engineering Fair, and I have been invited to the Intel ISEF at Pittsburgh in May 2012.

I am a distance runner, endurance biker and a classically trained dancer passionate about promoting healthful living in the community. As a member of the Alliance for a Healthier Generation, I am active in raising awareness about the epidemic of childhood obesity and poor sleep hygiene among teenagers.