Yu-Ru Liu

Exploring function fields

Yu-Ru Liu’s research focuses on additive and probabilistic number theory in function fields. A ring of polynomials over a finite field, called a function field, have analogues for a ring of integers. “Some operations that are difficult with integers become easy with polynomials, or vice versa,” she explains. “Or they have different characteristics, and require different approaches to tackle them.”

Yu-Ru examines comparative structures, properties and results of integers and polynomials through function fields, extending her work to other areas of mathematics to find connections and creative solutions. “I like seeing how wildly a result holds,” she notes. “I look at problems from a number theory point of view but also with probability and geometry to find a new perspectives.”

From Yu-Ru’s viewpoint, number theory is about exploration. The answers and the ride can be unpredictable. “We take our journey and see what happens,” she says. “Sometimes it can be wild. Sometimes it can be amazing. Sometimes you don’t know where you’ll go. But that’s part of the beauty of it.” Yu-Ru received the Canadian Mathematical Society (CMS) 2005 G. de B. Robinson Award for excellent papers published in the Canadian Mathematical Bulletin.

University of Waterloo Mathematics, Annual Report 2005