Undergraduate Mathematics Seminar
Cubic Curves and Surfaces, by Vladimir Uspenskiy (Ohio University, Mathematics)
What 


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