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Derived algebraic geometry and chromatic homotopy theory

Workshop
24th September 2018 to 28th September 2018

 

Workshop Theme

Chromatic homotopy theory is the classical subfield of algebraic topology which uses the theory of smooth one-parameter formal groups to organize calculations and the search for large-scale phenomena in stable homotopy theory. There is a formal group associated to any cohomology theory with Chern classes for complex vector bundles and, remarkably, the information can go the other way: under good conditions we can construct the cohomology theory from the formal group. This allows for a very tight connection between the geometry of formal groups and homotopy theory. For example, the moduli stack of formal groups has a height stratification, and thus induces a corresponding stratification in stable homotopy theory known as the chromatic filtration. Current major projects include calculations at a single height, assembling information from different heights, and the investigation of how various constructions in stable homotopy theory pass between heights.

If algebraic geometry is the study of schemes equipped with a sheaf of rings, then derived algebraic geometry is the study of schemes with sheaves of rings in some category amenable to homotopy theory, such as structured ring spectra. There are very important derived stacks and schemes that live over the moduli stack of formal groups, such as the moduli stack of generalized elliptic curves and certain Shimura varieties. This has led to a fruitful interplay between derived algebraic geometry and chromatic homotopy theory. Examples include the work of Gross and Hopkins establishing deep connections between various types of duality, the Hopkins-Miller work on topological modular forms, and considerable recent work on Picard and Brauer groups and spaces. This has expanded the field in new and unexpected directions.

 

Deadline for applications: 24th June 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.

Fees

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 23rd September 2018 to breakfast on Saturday 29th September 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

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

Meals

Lunch

Lunch will be served at Wolfson Court in the Cafeteria from 12:30 to 13:30 on days that lectures take place.

  • Accommodation Package and 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 at Wolfson Court
  • Other participants must purchase their meal using their dining card via the Porters' Lodge (forms can be found on the registration desk or at the Porters' Lodge)

Evening Meal

Participants are free to make their own arrangements for dinner.

Formal Dinner

The Formal Dinner will take place Wednesday 26th September at Trinity 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