Math’s Harvey wins NSF CAREER Award

Math’s Harvey wins NSF CAREER Award

BY JADE BOYD
Rice News Staff

Rice’s Shelly Harvey, assistant professor of mathematics, has won one of only eight CAREER grants awarded by the National Science Foundation (NSF) this year in the field of core mathematics.

SHELLY HARVEY

CAREER grants support early career development of junior faculty and are among the most competitive at NSF, which awards only about 400 of the five-year grants across all disciplines each year.

Typically ranging from $400,000 to $500,000, CAREER grants support the early career-development activities of scholars who are most likely to become academic leaders in their field.

“Shelly Harvey is a leader in applying techniques of noncommutative algebra to bear on problems of low-dimensional topology,” said Michael Wolf, professor and chair of the Department of Mathematics. “We of course are thrilled that, despite very stiff competition, the National Science Foundation recognized her unique abilities in this grant to support Professor Harvey’s development and innovative research and educational agenda.”

Harvey’s specialty is knot theory, a subfield of topology, the branch of mathematics that deals with explaining the spatial properties of objects. For scientists in many fields, the precise mathematical descriptions from topology are crucial. For example, some new cancer treatments are based on the knotting of cellular DNA, and astrophysicists can use the precise descriptions to contemplate the “shape” of space-time itself.

Harvey’s CAREER research project will go beyond the study of ordinary numbers and focus on more complex mathematical relationships that must be taken into account when building a precise mathematical description of things in the real world.

“Ordinary numbers are insufficient to capture the complexities of our world,” Harvey said.

As an example, Harvey cites a very simple example that most peoples learn as young children. When ordinary numbers are multiplied, the order of the numbers doesn’t matter. If A times B equals C, then B times A will also equal C. Multiplication of ordinary numbers is thus “commutative,” meaning the result will be the same regardless of the order of the terms.

However, in more complex mathematics, terms may not be commutative. For example, the multiplication of vectors and matrices is not.

“The physics of the 20th century has taught us that matter and energy cannot be described merely by numbers,” Harvey said. Rather, physical interactions are based on noncommutative algebra.

Harvey’s CAREER research project will investigate the role played by noncommutative algebra in a specific set of topological descriptions.

“This project is investigating how this noncommutative algebra yields a mathematical description of the geometric structure of 3-dimensional space and of objects in 3- dimensional space,” she said.