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Many people are fascinated by the idea of objects in four-dimensional space. In this talk, we investigate two important such objects: the hypercube (the analogue in 4-space of the cube) and the 3-sphere (the analogue of the sphere). By looking very carefully at 2- and 3-space, we can extrapolate properties of these 4-dimensional objects, and will will use computer animations to help understand them. Our end result will be to use the hypercube to visualize an important decomposition of the 3-sphere. The material should be accessible to students at all levels; there are no prerequisites. Differential Geometry Seminar
Some new tight immersions of surfaces in three-space
Davide Cervone, Union College
November 7, 1998
4:00 pm - 5:00 pm, Hylan 203

Tightness is a geometric property related to convexity. Some surfaces can be immersed in space having this property and others can't. Which ones can, and of the ones that can, in how many different ways? The answer to the first contains an important surprising result: the answer is different for polyhedral surfaces than it is for smooth surfaces. The second question depends on what we mean by "different", and is not yet completely answered for either type of surface. In this talk, we will discuss the current state of the subject, and will analyze several recent examples of tight polyhedral surfaces. Tea 3:30