The goal of the workshops was to introduce the necessary theory of D-modules, perverse sheaves, and Hodge structures to explain the very basics of Hodge modules. On the last day of the workshop, we applied this knowledge to birational geometry, specifically studying Hodge ideals introduced by Mustata and Popa. References for the workshop: 1. Hotta-Takeuchi-Tanisaki [D-modules, perverse sheaves, and representation theory](https://link.springer.com/book/10.1007/978-0-8176-4523-6) 2. Peters-Steenbrink [Mixed Hodge Structures](https://link.springer.com/book/10.1007/978-3-540-77017-6) 3. Schnell [Notes on Hodge modules](https://www.math.stonybrook.edu/~cschnell/pdf/notes/sanya.pdf) 4. Popa [A survey on geometric applications of Hodge modules](https://arxiv.org/pdf/1605.08093.pdf), and [another one](https://arxiv.org/pdf/1407.3294.pdf), and yet [another one but with focus on Hodge ideals](https://arxiv.org/pdf/1807.02375.pdf) 5. Mustata-Popa [Hodge ideals](https://arxiv.org/pdf/1605.08088.pdf) 6. Rui-Jie Yang [Notes on Hodge modules](https://drive.google.com/file/d/1xwMsQPwq30cHkOtb-73s1F6-oITb0z6j/view) > [!remark] > The main technical difficulty for the whole workshop was understanding the theory of D-modules well. Since we needed to rush through their theory, I strongly recommend reading more about D-modules in the excellent book: [D-modules, perverse sheaves, and representation theory](https://link.springer.com/book/10.1007/978-0-8176-4523-6). The first two days of the workshop were relatively independent of the third day. In fact, you only need to understand a small portion of the material from the first two days and blackbox everything else, and you can still, at least partially, understand the lecture notes from the last day. %% 2.1 --> 2.4 2.2 --> 2.4 2.3 --> 2.4 2.4 --> 3.1 --> 3.2 --> 3.3 1.3 --> 2.4 %% In what follows we provide a diagram explaining the connection between talks: ```mermaid graph TD A["1.1 D-modules"] --> B["1.2 Kashiwara"] --> C["1.3 Classification"] --> F["2.2 Riemann-Hilbert"] --> E["2.4 Hodge modules"] --> H["3.1 Hodge ideals"] --> I["3.2 Vanishing "] --> J["3.3 Birational definition"] D["2.1 Perverse sheaves"] --> E["2.4 Hodge modules"] G["2.3 Mixed Hodge structures"] --> E["2.4 Hodge modules"] D --> F ```