**University of Augsburg**

**October 2-6, 2023**

Synthetic algebraic geometry (SAG), is the study of algebraic geometry by synthetic means - instead of building up everything from ZF(C), we reason internal to a topos whose internal sets already contain the objects of interest. Our topos is called the (higher) Zariski topos and is given by Zariski-sheaves on affine schemes of finite type over an arbitrary base ring. **Higher** sheaves are neccessary to interpret the homotopy type theory we use to have, in addition to the usual convenience, an easy access to cohomology groups.

We have also begun to explore 𝔸¹-homotopy theory and algebraic stacks. The foundation is described here and more drafts can be found here.

All talks are in Building L (map below), room 2004. Coffee breaks will be in 2006.

The links below lead to videos hosted on this server, there is also a playlist on youtube.

Time | Mon | Tue | Wed | Thu | Fri |
---|---|---|---|---|---|

9:30 - 10:30 | Overview | Excursion | Cohomology I | Blow ups | Serre Affineness |

11:00 - 12:00 | HoTT+Modalities | Excursion | Smoothness I | Smoothness II | Stacks |

14:00 - 15:00 | Introduction to SAG | Excursion | Specific SAG | Stacks and 1-definite description | Cohomology I.5 |

15:30 - 16:30 | Constructive Equivalence of Functor of Points… | Excursion | Models | A1-homotopy theory | 2-Cats and Cosheaves |

**Note** that the excursion starts at 6:32am at the train station.

Here are some rough notes, who gave talks on which topic:

Speaker | Topic |
---|---|

Max Zeuner | Constructive Equivalence of Functor of Points and Topological Approach |

Hugo Moeneclaey | Smooth Schemes, Stacks, A1-homotopy theory |

Felix Cherubini | History and Overview, Cohomology, A1-homotopy theory |

Lukas Stoll | Modalities |

Nicolas Beck | Stacks and 1-definite description |

Matthias Hutzler | Introduction to Schemes, Models |

Marc Nieper-Wißkirchen | Blow ups (classically) |

Ingo Blechschmidt | Towards Specific Synthetic Algebraic Geometry, Serre Affineness |

Ilia Pirashvili | 2-Categories, Connected Components and fundamental groupoids as cosheaves |

Peter Arndt | Traditional A1-homotopy theory |

Ingo Blechschmidt | University of Augsburg |

Fabian Endres | University of Augsburg |

Matthias Hutzler | University of Gothenburg |

Felix Cherubini | University of Gothenburg |

Marc Nieper-Wißkirchen | University of Augsburg |

Lukas Stoll | University of Augsburg |

Hugo Moeneclaey | University of Gothenburg |

Max Zeuner | University of Stockholm |

Nicolas Beck | Freie Universität Berlin |

Heiko Braun | University of Bonn |

Tim Lichtnau | University of Bonn |

Peter Arndt (joining on Oct 3rd) | University of Düsseldorf |

Ilia Pirashvili | University of Augsburg |

- Marc Nieper-Wißkirchen, marc.nieper-wisskirchen@math.uni-augsburg.de

- Website: Felix Cherubini, felix.cherubini@posteo.de

First of all: **Google maps does not work** for public transport in Augsburg.

You can use this page, to figure out how to use public transport.

You can take tram 3 to get from the train station to campus.

The workshop is in the building L (L1 on the map):

The workshop dinner will be at the Indian restaurant Sangam:

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Register via email to Carolina Dujo (carolina.dujo@math.uni-augsburg.de). Let her know if you need a hotel room or financial support.

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If you need financial support to join the meeting, write an informal email to Marc Nieper-Wißkirchen to let us know.