A workshop on D-modules and their applications in algebraic geometry (05.03.2025 to 07.03.2025 at Ruhr-Universität Bochum).

Abstracts and a prospective timetable are available below.

If you wish to attend, please email christian.lehn(at)ruhr-uni-bochum.de timely. Registration is free of charge. Note that unfortunately, we are not able to offer funding for participants.

Abstracts

• Yajnaseni Dutta: Hodge modules related to Lagrangian fibrations of hyperkähler manifolds

Abstract to come.

• Andreas Hohl:The Stokes phenomenon - From rainbows to D-modules

In the theory of linear complex differential equations, an essential distinction is that between two types of singular points: While regular singularities have been well understood for a long time, the classification of irregular ones is much more recent. A key ingredient in the latter is the Stokes phenomenon, which was originally discovered by Stokes while performing computations in optics. It allows us to adapt the concepts of monodromy, local systems and perverse sheaves to the irregular case.

In this lecture series, we will learn about topological perspectives on systems with possibly irregular singularities that have been developed
in the last 50 years, and we will use them to explain some explicit results on Fourier transforms, an integral transform that is ubiquitious
in mathematics and physics. In the first lecture, we survey some basics about D-modules, and we are going to see in particular how to classify them via so-called Riemann-Hilbert correspondences. In the second lecture, we will learn about the Stokes phenomenon in the context of irregular singularities, and in particular different ways of representing it geometrically. In the final lecture, the Fourier transform will come into play, and we will investigate the question of how the Stokes data behave under this transform.

• Thomas Krämer: Perverse Sheaves on Abelian Varieties

To any perverse sheaf on an abelian variety one may attach a linear algebraic group by applying Tannaka duality to the tensor category generated by its convolution powers. The arising groups play a fundamental role in the geometry and arithmetic of irregular varieties. We will give a self-contained introduction to the topic starting from generic vanishing and the geometry of Gauss maps, and then discuss some recent applications in two directions: (1) Singularities of theta divisors and the moduli of abelian varieties, and (2) big monodromy results in arithmetic geometry.

Prospective timetable

The room is to be announced.

Organisation

• Cécile Gachet (RU Bochum)
• Daniel Greb (Universität Duisburg-Essen)
• Christian Lehn (RU Bochum)