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Describing Objects in Multiple Dimensions

University if Utah mathematician Christopher Hacon.

Lecturer: Christopher Hacon, distinguished professor of mathematics, University of Utah

Date: Wednesday, March 23, 2011

Time: 7:30 p.m.

Place: Aline Wilmot Skaggs Biology Building Auditorium, University of Utah


The study of polynomial equations and their solutions is one of the oldest endeavors in mathematics, dating to at least 500 B.C.

Christopher Hacon, a distinguished professor of mathematics at the University of Utah, will discuss how polynomial equations can be used to describe objects in multiple dimensions during a free public lecture on March 23.

Polynomial equations describe a wide range of problems in chemistry, engineering and physics, as well as economics and social sciences. Famous polynomial equations include linear equations, quadratic equations, Pythagorean Triples, Fermat’s Last Theorem and Kepler’s first and third laws of planetary motion.

Basic examples are the equations of a line, y = 2x + 1; a circle, x2 + y2 = 1; and a sphere, x2 + y2 + z2 = 1. Lines and circles are one-dimensional features drawn on a two-dimensional piece of paper and thus defined by an equation with two variables. Spheres are two-dimensional surfaces in a three-dimensional space and thus defined by an equation with three variables. A three-dimensional object could be defined by one equation in four variables, and so on.

Scientists usually study systems of many polynomials in many variables. The solutions often describe interesting geometric objects with many dimensions. In the two-dimensional case we have objects like spheres and doughnuts with one or more holes.

However, the greatest challenge is to understand the shapes of solutions in more than three dimensions. For example, string theory predicts that our universe has an additional six dimensions – beyond the four dimensions of space and time – with shapes given by special solutions to polynomial equations and sizes so small that they have not been observed yet. These higher dimensional shapes are very difficult to visualize and almost impossible to draw. By using algebraic methods, significant progress has been made on this problem in recent years.

Hacon was awarded a prestigious American Mathematical Society Centennial Research Fellowship during the 2006 academic year. In 2007, Hacon was among five mathematicians honored with a Clay Research Award, given by the Clay Mathematics Institute for “major breakthroughs in mathematics research.”

Hacon and Professor James McKernan of MIT received the 2009 American Mathematical Society’s Frank Nelson Cole Prize in Algebra for their groundbreaking work in algebraic geometry.

The Frontiers of Science lecture series is sponsored by the College of Science and the College of Mines and Earth Sciences. Lectures are free and open to the public, but tickets are required to guarantee seating. Visit to reserve tickets.

This news release and a photo of Hacon may be downloaded from: