Expert Details

Ryan Budney

Contact Information

Ryan Budney
associate Professor
Phone Number:
Languages: English
Mathematics & Statistics

Research Information

Research Description

-Geometric topology
-Manifold theory

Expertise Database

If you have a tangled piece of string with the ends glued together, is it possible to untangle it? How many ways can you untangle it? Can you change it to look exactly like another tangled piece of string?

How many ways can you move your hand? What is the shape of the space you need to make those movements?

Mathematician Ryan Budney asks questions like these through the study of topology--the study of the shape and space of things and the motions shapes can make. "It is sort of like the study of geometry," he says, "except that you are allowed to mess things up--deform them, bend them or twist them."

Although Dr. Budney's research is abstract, it is the base tool for many important innovations in areas such as robotics and even climate science. "We don't work on the end application," he says. "We work on the core ideas that are needed to get the application off the ground."

One application is found in the field of robotics. Today robots can play Ping-Pong, juggle or drive a car. To make this possible, their designers use topology to simplify our understanding of all possible states the robot can be in. Also, if the robot is in one location and wants to move to another, it has to know how to get around the obstructions in its way. These are topological problems.

"It has become increasingly suitable to apply topology to real-world problems," Dr. Budney says, "so it's having a growing impact on the world."

Related Links

Dr. Budney's Faces of UVic Research video:

Research Keywords

International Involvement

Countries lived/worked in

Australia, France, Germany, United States, Singapore

Software Development

Dr. Budney writes various software packages to aid in computation. The most substantial package that he contributes to is called Regina: