Counting points on surfaces
Is it possible to find more solutions for families of complex equations?
Since the Ancient Greeks we have known that there are an infinite number of solutions to Pythagoras' equation [a-squared plus b-squared equals c-squared] such as (3,4,5). However, we often know little about more complex equations. The researchers will examine families of equations for which they have recently demonstrated that there are far more solutions than people dared to believe until just a few years ago.