The conference is supported by a grant from the Trond Mohn foundation.

- Fernando Abellán (NTNU)
- Drew Heard (NTNU)
- Alice Hedenlund (NTNU)
- Hadrian Heine (Oslo)
- Achim Krause (Oslo)
- Clover May (NTNU)
- Marius Verner Bach Nielsen (NTNU)
- Torgeir Aambø (NTNU)

Thursday | |
---|---|

10:00-10:30 | Coffee |

10:30-11:15 | Aambø |

11:30-12:15 | Heine |

12:15-13:30 | Lunch |

13:30-14:15 | May |

14:30-15:15 | Abellán |

18:00 | Conference dinner |

Friday | |

09:45-10:30 | Krause |

10:30-11:00 | Coffee |

11:00-11:45 | Nielsen |

11:45-13:15 | Lunch |

13:15-14:00 | Hedenlund |

14:15-15:00 | Heard |

All talks will be held in room **KJL1** in the Kjelhuset building on NTNUs Gløshaugen campus in Trondheim.

**(∞,2)-Topoi and Descent***Fernando Abellán
(NTNU)*

(Joint with Louis Martini.)
This goal of this talk is to introduce the notion of
a Grothendieck (∞,2)-topos as a presentable (∞,2)-category satisfying
a categorified version of the descent axiom for (∞,1)-topoi of
Rezk-Lurie, which we call fibrational descent. As the name indicates,
fibrational descent axiomatizes the structure of internal fibrations
in an (∞,2)-category and it is closely related to the
straightening-unstraightening equivalence of Grothendieck-Lurie.
After presenting the main definition, I will give an overview of
several different ways of characterising 2-topoi, which includes a
2-dimensional version of Giraud's theorem. Moreover, I will show how
the theory of internal categories in an (∞,1)-topos (as develop by
Martini and Wolf) can be embedded into our formalism as (∞,1)-localic
2-topoi.
If time permits, I will explain how to construct a version of the
Yoneda embedding in an (∞,2)-topos and a theory of partially lax Kan
extensions.

**The spectrum of excisive functors***Drew
Heard (NTNU)*

We will explain a recent computation of the
Balmer spectrum of d-excisive functors from finite spectra to
spectra. We will spend the majority of the time trying to explain
exactly what this means. This is joint work with Arone, Barthel, and
Sanders.

**Twisted spectra***Alice Hedenlund
(NTNU)*

In the 90s, Cohen-Jones and Segal asked the
question of whether various types of Floer homology theories could be
upgraded to the homotopy level by constructing stable homotopy types
encoding Floer data. They also sketched how one could construct these
Floer homotopy types as (pro)spectra in the situation that the
infinite-dimensional manifold involved is “trivially polarized”. It
has since been realized that the correct home for Floer homotopy
types, in the polarized situation, is twisted spectra. This is a
generalization of parametrized spectra that one can roughly think of
as sections of bundles of categories whose fibre is the category of
spectra. In this talk, I will give an introduction to twisted spectra
and how to construct them formally within the ∞-categorical
framwork. In particular, I will cover the connection between twisted
spectra and modules over Thom spectra, as well as the 6-functor
formalism one obtains from looking at the total category of twisted
spectra over a fixed space (letting the twist vary). This is joint
work with T. Moulinos.

**A directed version of homotopy
colimits***Hadrian Heine (Oslo)*

In my talk
I will discuss a notion of lax colimit and lax limit for diagrams of
weak (∞, ∞)-categories thought of as directed homotopy
types. I will demonstrate that this notion is appropriate to perform
directed analogues of classical constructions of homotopy theory like
joins, suspensions, loop spaces and homotopy fibers, and therefore may
be thought of as a directed version of homotopy colimits and homotopy
limits. This is joint work with David Gepner.

**Algebraic K-theory and prismatic cohomology***Achim Krause (Oslo)*

In this talk I want to give an overview over recent work with Antieau and Nikolaus, about computing algebraic K-theory of **Z**/*p*^{n}.

**Classifying modules of equivariant Eilenberg–MacLane spectra***Clover May
(NTNU)*

Classically, since **Z**/*p* is a field, any module over the Eilenberg–MacLane spectrum H**Z**/*p* splits as a wedge of suspensions of H**Z**/*p* itself. Equivariantly, cohomology and the module theory of G-equivariant Eilenberg–MacLane spectra are much more complicated.
For the cyclic group G=C_{p} and the constant Mackey
functor __ Z/p__, there are infinitely many indecomposable
H

**On the Geometrization of Synthetic Spectra***Marius Verner Bach Nielsen (NTNU)*

Using ideas from spectral algebraic geometry, we produce a geometric setting for studying deformations of spectral sequences. One particular example of such a deformation is the category of synthetic spectra. We will end this talk by comparing synthetic Spectra with quasi-coherent sheaves on a certain geometric stack.

**Deformations of chromatic homotopy theory***Torgeir Aambø (NTNU)*

In recent years there has been significant interest in the deformation theory of stable ∞-categories. This has led to advances in computational results, as well as an increased structural understanding of these categories. In this talk we will survey some deformations relevant to the fundamental building blocks of stable homotopy theory — E(n)-local and K(n)-local spectra — and look at their interactions.