**CIRM VIRTUAL EVENT**

Interview at CIRM: Jorge Vitório PereiraJean Morlet Chair Holder - 2020/Semester 1 |
Varieties with Trivial Canonical ClassApril 13 to 17 JEAN-MORLET CHAIR - WORKSHOP Frank Loray (CNRS - Université de Rennes I)Jorge Vit ório Pereira (IMPA Brazil / Aix-Marseille Université)Erwan Rousseau (Aix-Marseille Université) The workshop aims at reviewing the recent decomposition theorem for singular varieties with trivial canonical class. This result is the culmination of efforts of a number of researchers and this workshop brings together most researchers which contributed to the proof of this result. We will also have some talks on the geometry of hyperkähler varieties. Due to the unusual circumstances, we have to experiment with a different format. The virtual workshop will consist of ten talks and two online sessions. Five of the talks figuring here are original from the Summer School on Foliations and Algebraic Geometry, which took place at Institut Fourier, Grenoble in from June-July 2019. The other five talks were recorded specially for the virtual workshop. On Tuesday, April 14, and on Thursday, April 16, we will host online sessions with the speakers of the conference with the possibility of online intervention by the registered participants of the workshop.SPEAKERSEkaterina Amerik (Université Paris-Sud) Arnaud Beauville (Université Nice Sophia-Antipolis) Stéphane Druel (CNRS, Université Lyon 1) Daniel Greb (University of Duisburg-Essen) Henri Guenancia (CNRS, Université Toulouse Paul-Sabatier) Andreas Höring (Université Nice Sophia Antipolis) |

**VIRTUAL DISCUSSIONS SCHEDULE**

**TUESDAY 14 APRIL**
Discussion session Speakers of the workshop will gather together online to discuss how the proof of the decomposition theorem came to be. |
**THURSDAY 16 APRIL**
3pm : Problem session Presentation of open problems on the subject, intertwined with comments by the speakers of the workshop. |

**Suggested order for watching the lectures**

The talk “Rational Curves and Contraction Loci on Holomorphic Symplectic Manifolds” by Ekaterina Amerik is independent of the other talks. The talk “The Decomposition Theorem: the Smooth Case” by Arnaud Beauville reviews the history of the decomposition theorem for smooth varieties and sketches its proof. All the other eight talks are about the decomposition theorem for varieties with singular canonical class. Below, one possible natural order to watch the nine lectures that discuss the decomposition theorem.

1. Beauville. The decomposition theorem: the smooth case

2. Greb. Structure theory for singular varieties with trivial canonical divisor

3. Guenancia. A decomposition theorem for singular spaces with trivial canonical class (part 1)

4. Guenancia. A decomposition theorem for singular spaces with trivial canonical class (part 2)

5. Guenancia. Holonomy of singular Ricci-flat metrics

6. Höring. A decomposition theorem for singular spaces with trivial canonical class (part 3)

7. Druel. A decomposition theorem for singular spaces with trivial canonical class (part 4)

8. Druel. A decomposition theorem for singular spaces with trivial canonical class (part 5)

9. Druel. A splitting theorem

**RECORDED TALKS - CIRM VIRTUAL CONFERENCES & INSTITUT FOURIER VIDEOS -**

**TOPICS OF DISCUSSIONS**

The decomposition theorem: the smooth caseBy Arnaud Beauville - Université Côte d'AzurA decomposition theorem for singular spaces with trivial canonical class (part 1)By Henri Guenancia - CNRS, Université Paul-Sabatier Holonomy of singular Ricci-flat metrics By Henri Guenancia - CNRS, Université Paul-Sabatier A decomposition theorem for singular spaces with trivial canonical class (part 4)By Stéphane Druel - CNRS - Université Claude Bernard Lyon 1 A splitting theorem By Stéphane Druel - CNRS - Université Claude Bernard Lyon 1 |
Structure theory for singular varieties with trivial canonical divisor By Daniel Greb - University of Duisburg-Essen A decomposition theorem for singular spaces with trivial canonical class (part 2)By Henri Guenancia - CNRS, Université Paul-Sabatier A decomposition theorem for singular spaces with trivial canonical class (part 3)By Andreas HöringA decomposition theorem for singular spaces with trivial canonical class (part 5)By Stéphane Druel - CNRS - Université Claude Bernard Lyon 1 Rational curves and contraction loci on holomorphic symplectic manifoldsBy Ekaterina Amerik - Université de Paris-Sud |