skip to content

Higher structures in homotopy theory


we have been made aware of a very convincing phone scam that is focusing on our workshop participants. Participants may be contacted by phone by a firm called Business Travel Management to arrange accommodation for workshops and/or programmes.  This includes a request to enter credit card information.

Please note, INI will never contact you over the phone requesting card details. We take all payments via the University of Cambridge Online store

If you have been contacted by this company please contact us as soon as possible.

2nd July 2018 to 6th July 2018
Stefan Schwede
Clark Barwick
Julie Bergner
Ieke Moerdijk

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.


Emily Riehl (Johns Hopkins University, 4 talks): The model-independent theory of (∞,1)-categories

Thomas Nikolaus (Universität Münster, 4 talks): Higher categories and algebraic K-theory

John Francis (Northwestern University, double talk): Factorization homology

Tobias Dyckerhoff (Bonn University, double talk): Higher Segal spaces

Rune Haugseng (University of Copenhagen)

Kathryn Hess (EPF Lausanne): Configuration spaces of fiber bundles

Chris Schommer-Pries (University of Notre Dame)

Sarah Yeakel (University of Maryland)

Andrew Blumberg (U Texas Austin)

Claudia Scheimbauer (University of Oxford)

Markus Spitzweck (Universität Osnabrück)


Deadline for applications: 02 April 2018

Apply now

Please note members of Cambridge University are welcome to turn up and sign in as a non-registered attendee on the day(s) during the workshop and attend the lecture(s). Please note that we cannot provide you with any support including name badge, meals or accommodation.

In addition to visiting the INI, there are multiple ways in which you can participate remotely.



Registration Only    
  • Registration Package: £230
  • Student Registration Package: £180

The Registration Package includes admission to all seminars, lunches and refreshments on the days that lectures take place (Monday - Friday), wine reception and formal dinner, but does not include other meals or accommodation.

Registration and Accommodation
  • Accommodation Package: £580

The Accommodation Package includes a registration fee, bed and breakfast accommodation at Churchill College from the evening of Sunday 1st July 2018 to breakfast on Saturday 7th July 2018, together with lunches and refreshments during the days that lectures take place (Monday - Friday). The formal dinner is also included, but no other evening meals.

Formal Dinner Only
  • Formal Dinner: £50

Participants on the Accommodation Package or Registration Package, including organisers and speakers, are automatically included in this event. For all remaining participants who would like to attend, such as programme participants, the above charge will apply.


Accommodation in single study bedrooms with shared facilities and breakfast are provided at Churchill College,



Lunch will be served in house on days that lectures take place.

Evening Meal

Participants are free to make their own arrangements for dinner.

Formal Dinner

The Formal Dinner will take place Wednesday 4th July at Emmanuel College. Participants on the Accommodation Package or Registration Package, including organisers and speakers, are automatically included in this event.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons