Title: How Small Can a Polynomial Be Near Infinity?
Speaker: János Kollár
Speaker Info: Princeton University
In this talk I discuss two parallel questions about polynomials. How small a polynomial can be near infinity and how quickly a polynomial can vanish near one of its zeros.Date: Friday, April 27, 2018
If we think only of polynomials of a single variable these questions are easy to answer, but as soon as we have two or more variables they acquire a surprising depth. I will focus on the two variable case, where a quite good bound can be proved using methods of basic algebra. We will end with a survey of open questions, many of which could be investigated using methods of undergraduate mathematics.