Department of

December 2013 January 2014 February 2014 Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 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 15 16 17 18 19 20 21 12 13 14 15 16 17 18 9 10 11 12 13 14 15 22 23 24 25 26 27 28 19 20 21 22 23 24 25 16 17 18 19 20 21 22 29 30 31 26 27 28 29 30 31 23 24 25 26 27 28

Wednesday, January 22, 2014

**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.