This autumn school will take place during the week September 17-21, 2018 in a conference center close to Utrecht, The Netherlands.

The idea of this autumn school is to bring together a group of about 25 participants in a remote place in order to learn about advanced topics in Algebraic Topology. The talks are meant to be accessible to first or second year PhD students.

Monday | Tuesday | Wednesday | Thursday | Friday | ||
---|---|---|---|---|---|---|

09:15-09:45 | Registration | |||||

09:45-10:45 | Pourcelot | 09:30-10:45 | Lawson 1 | Nikolaus 2 | Lawson 3 | Nikolaus 4 |

11:30-12:30 | Ariotta | 11:15-12:30 | Nikolaus 1 | Lawson 2 | Nikolaus 3 | Lawson 4 |

12:30 - 14:00 | Lunch | Lunch | Lunch | Lunch | Lunch | |

14:00-15:00 | Lundemo | Davies | Excursion | Questions | End | |

Reinhold | ||||||

15:15-16:15 | Hedenlund | 15:15-15:45 | Questions | Hedenlund | ||

16:45-17:45 | Fuentes | 16:15-17:45 | Gongshow | Gongshow | ||

19:00 | Dinner | Dinner | Dinner |

The following lecture series constitute the core program of the autumn school:

**Tyler Lawson**: Structured ring spectra*Abstract:*In these lectures we will discuss highly structured ring spectra: A-infinity algebras, E-infinity algebras, and those that interpolate between these concepts. Our main topics will include: classical examples that these unify, tools that are available with them, analogies and differences with classical homological algebra, invariants associated to them, and methods for constructing and analyzing them.**Thomas Nikolaus**: Topological Hochschild and cyclic homology*Abstract:*In this lecture series we will talk about two invariants of rings: topological Hochschild Homology (THH) and topological cyclic homology (TC). They were invented as a tool to study algebraic K-theory but have in recent years found independent applications. By definition THH is a higher algebraic analogue of the classical invariant Hochschild Homology which we will review first. Then we explain how working over the sphere spectrum (i.e. in the category of spectra) leads to THH. A crucial ingredient for the definition of TC is that THH, as opposed to ordinary Hochschild homology, admits Frobenius operators and we will explain their origin. Finally we will see how this naturally leads to the Definition of TC as a sort of 'Eigenspace' of the Frobenius operators and to the notion of a cyclotomic structure. We will complement the abstract definitions by explaining the basic calculations of these invariants, mostly for the case of the finite field F_p.

There will be additional talks providing background, and participants will have the chance to give short presentations about their own work.

**Hugo Pourcelot**: Introduction to infinity-categories**Stefano Ariotta**: The infinity-category of spectra**Tommy Lundemo**: Bar constructions in Algebra**Alice Hedenlund**: The Tate construction and spectral sequences**Daniel Fuentes**: Operads

**Jack Davies**: Algebraic and homotopical G_n-structures**Alice Hedenlund**: Multiplicative spectral sequences from infinity categories**Jens Reinhold**: Manifold bundles over surfaces and their characteristic numbers

The autumn school starts Monday September 17 in the morning and ends Friday 21 around noon, so it is recommended that you arrive already on Sunday September 16. Travel details will be given in due time before the autumn school.

The autumn school is organized by Gijs Heuts, Lennart Meier, Ieke Moerdijk, and Steffen Sagave.

The European Autumn School in Topology 2017 took place in September 2017, and the European Autumn School in Topology 2016 took place in September 2016.