Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, January 22, 2014.

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    December 2013           January 2014          February 2014
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1  2  3  4  5  6  7             1  2  3  4                      1
8  9 10 11 12 13 14    5  6  7  8  9 10 11    2  3  4  5  6  7  8
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Wednesday, January 22, 2014

4:00 pm in 245 Altgeld Hall,Wednesday, January 22, 2014

#### How many solutions does a polynomial have?

###### Zhiyu Tian (California Institute of Technology)

Abstract: A classical problem in number theory is to study whether a polynomial in several variables with rational coefficients has a solution in rational numbers. And in case there is a solution, what is the structure of the set of all solutions. An important idea in studying these problems is the so-called "local-global principle". Roughly speaking, this amounts to study the relation between solutions in rational numbers and solutions modulo a prime number. In this talk I will discuss the function field analogue of these problems and some recent advances in the subject.