Seminar of Algebra

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The Stokes Phenomenon for Irregular Singular $\mathcal{D}$-Modules

Hedwig Heizinger (Universität Augsburg)
Departamento de Álgebra
Fri, 16 may 2014 12:00
Hedwig Heizinger es estudiante de doctorado y asistente de investigación en la Universidad de Augsburg.

In my talk I want to give an introduction to the Stokes phenomenon as it appears in the theory of $\mathcal{D}$-modules.

After a short motivation, why irregular singular $\mathcal{D}$-modules come equipped with this additional structure (in contrast to regular singular ones!), we will examine basic examples in dimension one. This will lead to some - maybe new - important definitions and techniques: real oriented blow up of singularities, sheaf of moderate growth and rapid decay, moderate de Rham complex, Stokes sheaf.

From this point of view one may generalize to higher dimensions, such that I can give a short overview of my current research: Stokes structures and direct images of irregular singular $\mathcal{D}$-modules.