Spring 2012, Thursdays, Milner 216, 4:00-4:50 PM

Date: February 16

"  Real solutions for the discriminating mathematician! "
 Nick Hein  


How many real roots does a degree 42 univariate real polynomial have? You all know that it's more than -1, less than 43, and an even number. Some polynomial systems have added structure and we can say much more. I will describe situations where we have a polynomial of degree $d$, and we know that the lower bound on the number of real solutions is nontrivial. In some cases, the lower bound equals the upper bound. I will also show some examples when the geometry of the problem narrows down the possible values of $d$ in interesting ways.