## European Autumn School in Topology 2019

This autumn school will take place during the week September 16-20, 2019 in a conference center close to Utrecht, The Netherlands.

### Aims and Scope

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.

### Program

Monday Tuesday Wednesday Thursday Friday
09:15-09:45 Registration
09:45-10:45 Wu 09:30-10:45 Barthel 1 Salvatore 2 Barthel 3 Salvatore 4
11:30-12:30 Shi 11:15-12:30 Salvatore 1 Barthel 2 Salvatore 3 Barthel 4
12:30 - 14:00LunchLunchLunchLunchLunch
14:00-15:00 Ariotta Bellumat Excursion Taggart End
Blom Zeng
15:15-16:15 Reinhold 15:15-15:45 Questions Questions
16:45-17:45 Sikora 16:15-17:45 GongshowGongshow
19:00DinnerDinnerDinner

### Lecture series

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

• Tobias Barthel: Chromatic structures in stable homotopy theory

#### Tentative Abstract:

Chromatic homotopy theory acts like a prism for the stable homotopy category: it reveals how it decomposes into irreducible layers and moreover offers tools for understanding and reassembling these constituent pieces. The goal of these lectures is to give an overview of the chromatic perspective on stable homotopy theory. Beginning with the Ravenel conjectures, we will discuss some of the key features of chromatic homotopy theory and then describe a selection of recent developments, including the chromatic splitting conjecture, asymptotics, and connections to equivariant homotopy. Finally, we will explore similar chromatic patterns in other contexts like modular representation theory and outline a common framework for studying them.
A list of references can be found here.

• Paolo Salvatore: $$E_n$$ operads and configuration spaces

#### Tentative Abstract

Preliminaries are basic notions of algebraic topology and complex analysis. A list of references can be found here.

• Lecture 1 Deligne conjecture. The cacti complex and its action on the Hochschild complex.
• Lecture 2 The light cone cell decomposition of the configuration spaces and moduli spaces. Cells correspond to trees labelled by cacti.
• Lecture 3 The Fulton Mac Pherson compactification and operad. Connections to moduli spaces of stable curves and/or embedding calculus.
• Lecture 4 Resolutions of operads. The W construction and the Fulton Mac Pherson operad. Construction of the operadic cell decomposition.

### Preparatory talks

• Yuqing Shi: Spectra
• Stefano Ariotta: The stable homotopy category
• Jens Reinhold: Configuration spaces
• Igor Sikora: Complex orientable ring spectra
The topics of the preparatory talks including references are listed here.

### Contributed talks

• Nicola Bellumat: Iterated chromatic localization
• Thomas Blom: Parametrized operads and the derivatives of the identity functor
• Niall Taggart: Comparisons between versions of functor calculi
• Mingcong Zeng: Dual Steenrod algebra and real cobordism

### Registration

The registration deadline has passed, and registration is no longer possible.

### Travel Information

The autumn school starts Monday September 16 in the morning and ends Friday 20 around noon, so it is recommended that you arrive already on Sunday September 17. Travel details will be given in due time before the autumn school.

### Organizers

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

### Previous schools

Previous editions of this autumn school took place in 2018, in 2017, and in 2016.