Rice University Department of Mathematics Colloquium

Differential Galois Extensions and Patching

4:00 pm Thursday, November 3rd, 2016
Julia Hartmann (University of Pensylvania)

Abstract: Differential Galois theory is an algebraic theory for linear differential equations, in analogy to classical Galois theory. It was proposed by Picard and Vessiot almost a hundred years ago and then developed by Kolchin. Patching techniques have been used in inverse Galois theory and more recently in other areas of algebra and arithmetic geometry. The talk gives an introduction to differential Galois theory and to patching. Using patching methods, we will deduce new properties of differential Galois extensions over function fields of Riemann surfaces.

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