# CMS Jeffery-Williams Prize

**The CMS Jeffery-Williams Prize was inaugurated to recognize mathematicians who have made outstanding contributions to mathematical research.** The first award was presented in 1968 and is named after Ralph Jeffery (1889-1975) and Lloyd Williams (1888-1976), who were two influential CMS board members.

Ralph Jeffery was the fourth president of the Canadian Mathematical Society from 1957-1961. Though he left school in the middle of Grade 8 to join his father as a fisherman, he graduated from Acadia University in 1921 and completed his Ph.D. in mathematics at Cornell in 1928. He served as Head of Mathematics at Acadia from 1924-1942 and Head of Mathematics at Queen's University from 1942 until his retirement in 1960. He then returned to an active teaching role at Acadia until his death, teaching three full courses in his 85th year. A dedicated member of the Canadian Mathematical Congress, he established its popular Summer Research Institute (SRI) which he directed each year from 1950-1965. By creating the SRI and by consistently encouraging research he made an outstanding contribution to mathematics in Canada.

Lloyd Williams was the treasurer of the CMS from 1945-1965. He taught at McGill University from 1924 until his retirement in 1954. Lloyd's vision of a forum which would bring Canadian mathematicians together contributed greatly to the formation and success of the Canadian Mathematical Congress. He oversaw the financial development of the Congress, securing donations from a wide variety of government, corporate and individual sources. As well, he worked hard to ensure that the Congress served all members of the mathematical community equally. He was the first to supervise a Ph.D. thesis in mathematics for a black student.

- Sunday, Jul 23 [Symposia (Auditorium), Centre Mont Royal]
- 19:00 Robert McCann (University of Toronto, Canada), Optimal transport between unequal dimensions

For information about past recipients visit: Jeffery-Williams Prize

Robert McCann

University of Toronto, CanadaMcCann is an internationally recognized expert in applied mathematics at the forefront of the development of the theory and applications of optimal transportation. Together with his collaborators and peers worldwide, he has led a renaissance in the theory of optimal transportation, helping to transform it into one of the most vibrant and exciting areas in mathematics today.

Optimal transport between unequal dimensionsIn the last few decades, the theory of optimal transportation has blossomed into a powerful tool for exploring applications both within and outside mathematics Its impact is felt in such far flung areas as geometry, analysis, dynamics, partial differential equations, economics, machine learning, weather prediction, and computer vision. The basic problem is to transport one probability density onto other, while minimizing a given cost c(x,y) per unit transported. In the vast majority of applications, the probability densities live on spaces with the same (finite) dimension. After briefly surveying a few highlights from this theory, we focus our attention on what can be said when the densities instead live on spaces with two different (yet finite) dimensions. Although the answer can still be characterized as the solution to a fully nonlinear differential equation, it now becomes badly nonlocal in general. Remarkably however, one can identify conditions under which the equation becomes local, elliptic, and amenable to further analysis.