3:30 p.m.
Liouvillian extensions and the Galois theory of linear differential equations
Varadharaj Srinivasan
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18-04-12

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Abstract

Let F be a differential field and let E be a differential field extension of F with no new constants. We say that E is a liouvillian extension of F if there is a tower of differential field extension F = F_0 \subset F_1 \subset .... \subset F_n = E such that F_i = F_{i-1}(x_i) where (x_i)' belongs to F_{i-1} or (x_i)'/x_i belongs to F_{i-1} or x_i is algebraic over F_{i-1}. In this talk, we will study the structure of certain class of liouvillian extensions and discuss the role it plays on the Galois theory of linear differential equations and on the theory of integration in finite terms.