**Title:** How Small Can a Polynomial Be Near Infinity?

**Speaker:** János Kollár

**Speaker Info:** Princeton University

**Brief Description:**

**Special Note**:

**Abstract:**

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.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.

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