Seminar Algebra and Geometry: Luca Studer (University of Bern)

Equations with complex analytic coefficients

In the talk we discuss how Oka theory helps to solve systems of equations with complex analytic entries. A classical example is the fact that for every pair of complex analytic functions a, b: C^n -> C with no common zero there are complex analytic functions x, y: C^n -> C satisfying the Bézout identity ax+by=1. A more recent example is Leiterer's work, where the solvability of xax^{-1}=b for complex analytic matrix-valued maps a, b: C^n -> Mat(n x n, C) is investigated. Both examples are brought into the context of the speakers research.

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