Sixth Monroe Martin Prize Awarded at College ParkJune 10, 2001
Monroe Martin, on hand in March for the sixth presentation of the prize established in his honor by the University of Maryland, is shown here with this year's prize recipients: Robert McCann (left) and Yury Grabovsky (right).
Grabovsky was honored for his paper "Exact Relations for Effective Tensors of Polycrystals. I. Necessary Conditions," which appeared in Archive for Rational Mechanics and Analysis (Vol. 143, 1998). In the paper Grabovsky describes a general method for finding all exact relations for effective moduli of polycrystals, by reducing it to an algebraic problem of characterizing the rotationally invariant families of Jordan algebras. The method is applicable to a variety of physical settings, including elasticity, thermo-elasticity and piezo-elasticity. Grabovsky was an undergraduate and graduate student at New York University, from which he received a PhD in 1994.
"Exact Solutions to the Transportation Problem on the Line," the paper for which McCann was selected, appeared in Proceedings of the Royal Society of London (Vol. A455, 1999). This paper analyzes the solution of a classical optimization problem that was formulated by Monge in 1781. Couched in an economic setting, the problem is as follows: Given a distribution of iron mines, and a distribution of factories that require iron ore, decide how the mines should supply the ore to the factories so as to minimize the total transportation costs. When the cost is a strictly concave increasing function of the distance traveled, this problem has a unique, geometrically characterized solution with a hierarchical structure. The paper elegantly exploits this structure in the one-dimensional setting to derive an algorithm that obtains the solution by a combinatorial sequence of finite-dimensional optimizations involving convex, separable network flows. McCann received his PhD from Princeton University in 1994.
The Monroe H. Martin prize was established to honor the outstanding contributions of Monroe H. Martin, a professor emeritus at the University of Maryland, College Park. Martin chaired the Department of Mathematics from 1942 until 1954 and was the founding director of the Institute for Fluid Dynamics and Applied Mathematics (a forerunner of the Institute for Physical Sciences and Technology) from 1952 until 1968. As on the five previous occasions, Martin, who is now in his 95th year, presented this year's awards.