# Higher structures in homotopy theory

Created: | 2018-07-03 11:16 |
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Institution: | Isaac Newton Institute for Mathematical Sciences |

Editors' group: | Members of "Isaac Newton Institute for Mathematical Sciences". |

Description: | Workshop
2nd July 2018 to 6th July 2018 Organisers: Stefan Schwede Rheinische Friedrich-Wilhelms-Universität Bonn Clark Barwick University of Edinburgh Julie Bergner University of Virginia Ieke Moerdijk Universiteit Utrecht Workshop Theme Homotopy theory has covered a long distance since its origins, the classification of spaces up to homotopy equivalence. Over the years, various kinds of mathematical structures have been investigated from a homotopical perspective, such as equivariant spaces, rings, C^*-algebras, or varieties. Many different approaches of how to formalize what a “homotopy theory” is were proposed, the most prominent ones being the notions of model category and ∞-category. The relationship between the different ways to formalize a homotopy theory is now well understood; indeed, for comparing different concepts of homotopy theories, one often wants to consider all of them together as another homotopy theory, i.e., a ‘homotopy theory of homotopy theories’. Somewhat surprisingly, most of the concepts organize themselves into a Quillen model category, and the various approaches are Quillen equivalent. After these individual comparison results, Töen was even able to axiomatically characterize a homotopy theory of homotopy theories. The homotopy theory of homotopy theories is only the first step in a hierarchy of interesting structures, namely the homotopy theoretic approach to higher categories. From this broader perspective, homotopy theories are just (∞, 1)-categories, where the ∞ indatices a structure with higher morphisms of all levels, and the 1 refers to the fact that all 1-morphisms and higher morphisms are weakly invertible. There are now ways to give rigorous meaning to the notion of (∞, n)-categories i.e., where only higher morphisms in level n and above are invertible. Having a rigorous model category of (∞,n)-categories is a cornerstone for the modern approach to topological field theory, thereby unifying categorical considerations with those of homotopy and manifold theory. This workshop consists of lecture series as well as individual research talks. The introductory series will explain some of the key methods relevant to many parts of the overarching program; they are intended to invite graduate students and postdocs into the field, as well as to strengthen the common ground of the program participants. The individual talks will inform us about recent developments about higher structures in homotopy theory. |

# Media items

This collection contains 97 media items.

### Media items

#### Configuration spaces and Lie algebras away from characteristic zero

51 views

Knudsen, B

Thursday 6th December 2018 - 11:30 to 12:30

**Collection**:
Higher structures in homotopy theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Mon 10 Dec 2018

#### Hermitian K-theory for Waldhausen infinity categories with genuine duality

29 views

Spitzweck, M

Friday 6th July 2018 - 11:30 to 12:30

**Collection**:
Higher structures in homotopy theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 6 Jul 2018

#### The model-independent theory of (∞,1)-categories (1)

128 views

Riehl, E

Monday 2nd July 2018 - 10:00 to 11:00

**Collection**:
Higher structures in homotopy theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 3 Jul 2018

#### A Künneth theorem for configuration spaces of products

44 views

Hess, K

Thursday 5th July 2018 - 16:00 to 17:00

**Collection**:
Higher structures in homotopy theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 6 Jul 2018

#### Adelic models for Noetherian model categories (joint work with John Greenlees)

24 views

Balchin, S

Tuesday 2nd October 2018 - 14:00 to 15:00

**Collection**:
Higher structures in homotopy theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 3 Oct 2018

#### Algebraic models for rational equivariant commutative ring spectra

42 views

Kedziorek, M

Tuesday 14th August 2018 - 11:30 to 12:30

**Collection**:
Higher structures in homotopy theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 15 Aug 2018

#### Ambidexterity in the T(n)-Local Stable Homotopy Theory

39 views

Yanovski, L

Tuesday 28th August 2018 - 15:30 to 16:30

**Collection**:
Higher structures in homotopy theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Mon 3 Sep 2018

#### An Additivity Theorem for cobordism categories, with applications to Hermitian K-theory

12 views

Steimle, W

Tuesday 21st August 2018 - 14:00 to 15:00

**Collection**:
Higher structures in homotopy theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 23 Aug 2018

#### An introduction to topological coHochschild homology

53 views

Hess, K

Tuesday 6th November 2018 - 15:30 to 16:30

**Collection**:
Higher structures in homotopy theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 7 Nov 2018

#### C_2 equivariant homotopy groups from real motivic homotopy groups

15 views

Behrens, M

Thursday 16th August 2018 - 09:00 to 10:00

**Collection**:
Higher structures in homotopy theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 17 Aug 2018

#### Configuration spaces of points and real Goodwillie-Weiss calculus

35 views

Willwacher, T

Tuesday 4th December 2018 - 10:00 to 11:00

**Collection**:
Higher structures in homotopy theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 5 Dec 2018

#### Connectivity and growth in the homology of graph braid groups

11 views

Knudsen, B

Tuesday 10th July 2018 - 14:00 to 15:00

**Collection**:
Higher structures in homotopy theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 11 Jul 2018

#### Contributed talk - Extended evaluation maps from knots to the embedding tower

24 views

Kosanović, D

Thursday 6th December 2018 - 16:30 to 17:00

**Collection**:
Higher structures in homotopy theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 14 Dec 2018

#### Contributed Talk - The low dimensional homology of Coxeter groups

14 views

Boyd, R

Thursday 6th December 2018 - 15:00 to 15:30

**Collection**:
Higher structures in homotopy theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Mon 10 Dec 2018

#### Derived algebraic geometry I

189 views

Antieau, B

Wednesday 26th September 2018 - 10:00 to 11:00

**Collection**:
Higher structures in homotopy theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 26 Sep 2018

#### Derived algebraic geometry II

56 views

Antieau, B

Thursday 27th September 2018 - 10:00 to 11:00

**Collection**:
Higher structures in homotopy theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 28 Sep 2018

#### Derived modular envelopes and moduli spaces of bordered Riemann surfaces

16 views

Berger, C

Tuesday 31st July 2018 - 14:00 to 15:00

**Collection**:
Higher structures in homotopy theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 1 Aug 2018

#### Duality and invertibility using finite resolutions - 2

169 views

Beaudry, A

Tuesday 25th September 2018 - 10:00 to 11:00

**Collection**:
Higher structures in homotopy theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 26 Sep 2018

#### Dualizability in the higher Morita category

25 views

Scheimbauer, C

Friday 6th July 2018 - 10:00 to 11:00

**Collection**:
Higher structures in homotopy theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 6 Jul 2018

#### Embeddings, operads, graph-complexes

17 views

Turchin, V

Tuesday 4th December 2018 - 14:30 to 15:30

**Collection**:
Higher structures in homotopy theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 5 Dec 2018