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3rd December 2018 to 7th December 2018
Ulrike Tillmann University of Oxford
David Ayala Montana State University
Oscar Randal-Williams University of Cambridge
Michael Weiss Universität Münster

Workshop Theme:

The relationship between the topology of manifolds and homotopy theory has been recently strengthened in several ways, harking back to the close connection which existed between these subjects in their early development. 

One direction has been the circle of ideas arising from Madsen--Weiss' proof of Mumford's conjecture, with cobordism theory attracting new interest in the modern guise of cobordism categories, and applications to the study of automorphism groups of manifolds by a method quite different to the classical route, via surgery theory, pseudoisotopy theory, and Waldhausen's algebraic K-theory of spaces. Another direction, related to the previous one, is Lurie's development of a close connection between extended Topological Quantum Field Theories and ideas from the homotopy theory of higher categories, where the theory of manifolds may be encoded as a universal object in higher category theory. A third direction, again related to the previous one, is the notion of factorisation homology. This is a pairing between n-manifolds and n-categories: regarded as an invariant of manifolds, it is a promising source of sensitive manifold and linking invariants; regarded as an invariant of higher categories, it codifies their infinitesimal structure.  

This workshop will bring together mathematicians working at the forefront of these and related areas, to develop new foundational results, pursue applications, and relate these new ideas with more classical work in the topology of manifolds.

Speakers will include:

  • David Ben-Zvi    
  • Ryan Budney      
  • Diarmuid Crowley 
  • Johannes Ebert   
  • Soren Galatius   
  • Andre Henriques  
  • Alex Kupers      
  • Chris Schommer-Pries
  • Victor Turchin   
  • Thomas Willwacher
  • Nathalie Wahl 


Deadline for applications: 2nd September 2018

HHH programme participants DO NOT need to apply, programme participants with visit dates during HHHW04 will automatically be added to the attendee list.

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.

Apply now


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.

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.


Unfortunately we do not have any accommodation to offer so all successful applicants will need to source their own accommodation.  Please see the Hotels Combined website for a list of local hotels and guesthouses.



Lunch will be served at Churchill College in the Cafeteria on days that lectures take place.

  • Registration Package participants should present their badge as payment for their meal
  • Those issued with a blue Institute door entrance card can add money onto the card via the Porters' Lodge
  • Other participants can purchase their meal using cash
Evening Meal

Participants are free to make their own arrangements for dinner.

Formal Dinner

The Formal Dinner will take place Wednesday 5th December at Christ's 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