FRONTIERS OF SCIENCE LECTURE WED, FEB. 1 "Describing Shapes and Spaces Beyond Three Dimensions" --- --- 7:30 PM ALINE W. SKAGGS BIOLOGY BLDG. (See map: http://www.map.utah.edu/index.html?find=82) FREE AND OPEN TO THE PUBLIC! NO TICKETS REQUIRED Over the last 100 years, topology, a branch of geometry, has become a major focus of mathematicians and scientists. Topologists study what properties of objects and shapes remain the same even when shapes are stretched and distorted. For instance, a square can be “squeezed” into a circle, but not into a perfectly straight line, or a sphere. In 1905 Henry Poincaré, the leading mathematician of his day, proposed the study of spaces beyond the three visible dimensions, and described a problem about the simplest example of a higher-dimensional space: the sphere. This problem became known as the Poincaré Conjecture and was the most important problem in 20th century topology. Demonstrating how challenging it is to understand higher-dimensional spaces the Poincaré Conjecture challenged mathematicians for nearly 100 years! Professor Morgan’s lecture will discuss what the notions of “dimension,” “shape,” and “space” refer to in topology, the tricks topologists use to describe these concepts, and how these methods and techniques apply to higher-dimensional spaces. Morgan also will explain the Poincaré Conjecture: what it says about spheres, and how it has been applied to all three-dimensional spaces. This event is free and open to the public! NO tickets are required. Arrive early for best seating.