## Seminar: Topics in (∞,2)-categories

During the Summer semester 2023, I organized a seminar on Topics in (∞,2)-categories. We had an overview of different models of (∞,2)-categories, as well as some constructions thereof, such as the Gray tensor product and (∞,2)-limits. We also considered some applications of (∞,2)-category theory in derived algebraic geometry, topological quantum field theory, and K-theory.

Here is a detailed program of the seminar.

April 19 | 2-categories and double categories | Benedikt Froehlich |
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April 26 | (∞,1)-categories and enriched models of (∞,2)-categories | Jana Nickel |

May 3 | Model of complete Segal $\Theta_2$-spaces | Marco Giustetto |

May 10 | Models of double ∞-categories and 2-fold complete Segal spaces | Divya Ghanshani |

May 17 | Model of scaled simplicial sets | Jana Nickel |

May 24 | Gray tensor product for 2-categories | Vikram Nadig |

May 31 | Gray tensor product for (∞,2)-categories | Jun Xu |

June 7 | Universal property of the (∞,2)-category of correspondences | Johannes Glossner |

June 14 | Limits in a 2-category | Lyne Moser |

June 21 | The fully extended 2-dimensional cobordism hypothesis | Pier-Federico Pacchiarotti |

June 28 | Six functor formalism | Johannes Glossner |

July 5 | Functoriality of the stable $A_1$-homotopy category | Niklas Kipp |

July 12 | Limits in an (∞,2)-category | Nima Rasekh |

July 19 | K-theory via double categories | Maru Sarazola |