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Daily Overview |
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D-M1: D-Modules: Bridging Theory and Applications Location: M630 Session Chair: Andreas Hohl Session Chair: Anna-Laura Sattelberger | |
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Relative regular $\mathcal D$-modules and their Geometric Applications 1: University of Padua, Italy; 2: University of Lisbon, Portugal; 3: Ecole Polytechnique, CNRS, France The theory of relative $\mathcal D$-modules provides a natural algebraic framework for studying families of linear partial differential equations, where the parameter space $S$ is a complex manifold of arbitrary dimension. In this talk, based on joint works with Teresa Monteiro Fernandes and Claude Sabbah, we discuss the property of regularity for relative $\mathcal D$-modules and its stability under fundamental geometric functors, such as direct image, pullbacks and duality. We will highlight how this relative approach—culminating in the relative regular Riemann-Hilbert Correspondence provides useful algebraic tools for investigating the behavior of differential systems under deformations. | |
