# Birkar, Cascini, Hacon, and McKernan to receive 2016 AMS Moore Prize

November 30, 2015Caucher Birkar (University of Cambridge), Paolo Cascini (Imperial College London), Christopher D. Hacon (University of Utah), and James McKernan (UC San Diego) will receive the 2016 AMS E. H. Moore Research Article Prize. They are honored for their article "Existence of minimal models for varieties of log general type,"

*Journal of the AMS*(2010).

The work of these four authors is in algebraic geometry, a branch of mathematics that investigates connections between numbers and shapes. A central notion is that of an algebraic variety, which is the solution set of a collection of polynomials. That solution set can be thought of as a geometric object, and the main motivation is to understand how the algebraic properties of the polynomials translate into geometric properties of the corresponding algebraic variety.

The "minimal model program," which grew out of the work of Shigefumi Mori (Fields Medal, 1990) and others, has stimulated a great deal of research in algebraic geometry over the past 30 years. The aim of the program is to find a way of classifying algebraic varieties by finding representations of them that are in some sense the best, or simplest, representations. (See "What is a Minimal Model?" by János Kollár,

*Notices of the AMS*, March 2007.)

Birkar, Cascini, Hacon, and McKernan made a major stride in advancing the minimal model program. The article cited above, together with its companion "Existence of minimal models for varieties of log general type II" by Hacon and McKernan, which appeared in the same issue of the

*Journal of the AMS*, transformed research within the minimal model program. "Experts agree that the article together with its companion mark a watershed in algebraic geometry," the prize citation says.

Presented every three years, the Moore Prize is awarded for an outstanding research article that appeared in one of the AMS primary research journals in the previous six years. The prize will be presented on Thursday, January 7, 2016, at the Joint Mathematics Meetings in Seattle.

Find out more about AMS prizes and awards at http://www.ams.org/profession/prizes-awards/prizes.

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Founded in 1888 to further mathematical research and scholarship, today the American Mathematical Society fulfills its mission through programs and services that promote mathematical research and its uses, strengthen mathematical education, and foster awareness and appreciation of mathematics and its connections to other disciplines and to everyday life.American Mathematical Society

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