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Equivariant and motivic homotopy theory


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13th August 2018 to 17th August 2018
Daniel Isaksen
John Greenlees
Kyle Ormsby
Charles Rezk

Scientific Advisory Panel: Nora Ganter (Melbourne) and Inna Zakharevich (Cornell) 

Workshop Theme 

Equivariant and motivic homotopy are two of the most active areas in algebraic topology, bringing together researchers in topology, algebra, representation theory, and algebraic geometry. Equivariant homotopy theory has been a fundamental component of algebraic topology since its inception. The Sullivan and Segal conjectures explored how to understand homotopy fixed points unstably and stably, and trace methods in algebraic K-theory are one of the most successful approaches to computing algebraic K-groups. More recently, equivariant homotopy has experienced an exciting renaissance featuring applications to geometry.  These include the solution by Hill-Hopkins-Ravenel of the Kervaire invariant one problem and Manolescu's solution of the triangulation conjecture. Though a newer area, motivic homotopy is a hugely active research field, bringing together ideas in algebraic topology and algebraic geometry. From Voevodsky's proof of the Milnor conjecture to the Rost-Voevodsky proof of Block-Kato, motivic homotopy theory has significantly impacted algebraic geometry.

This workshop will bring together researchers interested in these exciting areas, exploring new mathematics and discussing deep foundational work. Additionally, there are significant and subtle interactions between equivariant and motivic homotopy, with each providing intuition and strategies of proof for the other. We hope to further develop and build upon these connection. 

Deadline for applications: 13th May 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 12th August 2018 to breakfast on Saturday 18th August 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 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 15th August at Gonville and Caius 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