Undergraduate Mathematics Seminar
Cubic Curves and Surfaces, by Vladimir Uspenskiy (Ohio University, Mathematics)
Feb 13, 2013
from 04:10 PM to 04:55 PM
|Where||226 Morton Hall|
|Contact Name||Martin Mohlenkamp|
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Abstract: Second-degree polynomials determine well-known curves on the plane (ellipses, parabolas, hyperbolas) and surfaces in the 3-space (paraboloids and hyperboloids of various kinds, etc.). Plane curves that can be determined by a third-degree polynomial, known as elliptic curves, are the topic of much of current research. One of the millennium million-dollars problems deals with them. In the talk, I'll discuss some applications of third-degree curves to plane geometry and number theory. I'll also sketch the proof of the "27 lines theorem": for every smooth third-degree surface in the complex projective 3-space there are exactly 27 lines lying on it.