Seminar organised by Giulio Orecchia (g [dot] orecchia [at] math [dot] leidenuniv [dot] nl), Raymond van Bommel (r [dot] van [dot] bommel [at] math [dot] leidenuniv [dot] nl) and Erik Visse (h [dot] d [dot] visse [at] math [dot] leidenuniv [dot] nl)

Thanks to Jinbi Jin for providing the template of this webpage.

Meeting 0: Thursday 10 September, 10:30-11:00, common room

Meeting 1: Thursday 24 September, 09:45-11:30, room B03

Meeting 2: Friday 9 October, 10:00-12:00, room B03

Meeting 3: Thursday 15 October, 09:45-11:30, room B03

Meeting 4: Friday 23 October, 11:00-13:00, room B03

Meeting 5: Friday 30 October, 11:00-13:00, room 302-304

Meeting 6: Wednesday 4 November, 11:00-13:00, room B03

Meeting 7: Friday 20 November, 11:00-13:00, room B03

Meeting 8: Wednesday 2 December, 15:00-17:00, room B03

See program below. We will treat the algebraic stack \(\mathcal{M}_g\), look at the definition, properties, some applications and maybe its compactification.

- Categories fibered in groupoids, descent, \(\mathcal{M}_g\) as a stack
- \(\mathcal{M}_g\) as algebraic stack
- Deformation theory, relative dimension of \(\mathcal{M}_g\) over \(\mathrm{Spec}(\mathbb{Z})\), smoothness of \(\mathcal{M}_g\)

We will also aim to treat at least one (but hopefully multiple) of the following topics.

- Applications of stack theory
- Compactification of \(\mathcal{M}_g\)

- To learn about Grothendieck topologies and more:
*Étale cohomology seminar*→ Jinbi Jin *Stacks Project*→ colombia.edu- A. Vistoli,
*Notes on Grothendieck topologies, fibered categories and descent theory*→ arxiv.org - Harris,
*Moduli of curves* - Vakil, Olsson, Lieblich et al.,
*Deformation theory and moduli*

25 September | Giulio Orecchia | The moduli stack \(\mathcal{M}_g\)→ Giulio Orecchia |

9 October | Raymond van Bommel | The algebraic stack \(\mathcal{M}_g\)→ Raymond van Bommel |

15 October | Carlo Pagano | Some very basic deformation theory→ Carlo Pagano |

23 October | David Holmes | Moduli of stable curves→ David Holmes |

30 October | David Holmes / Erik Visse | Continuation of last week's talk / Introduction to stable maps→ Erik Visse |

4 November | Erik Visse | Kontsevich' formula for rational curves in the plane |

20 November | Giulio Orecchia | Gromov-Witten invariants→ Giulio Orecchia |

2 December | David Holmes | Quantum cohomology→ David Holmes |