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Geometry and Model Theory

Time: Friday, November 04, 2011, 14h - 15h30

Location: amphithéâtre Rataud

Inverse problems in the Parameterized Picard-Vessiot Theory

Michael Singer (North Carolina, SU)

The parameterized Picard-Vessiot theory aims at studying the differential behavior of solutions of parameterized linear differential equations. It associates to such an equation a linear differential algebraic group (LDAG), that is, a group of matrices whose entries are functions satisfying a fixed set of differential equations. After giving an introduction to this theory, I will show that not all LDAGs can occur as Galois groups over k(x), the field of rational functions in x whose coefficients are functions of a parameter t and characterize those LDAGs that do occur.

 

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