Felix Klein Lectures

Elliptic cohomology and elliptic curves

Speaker: Charles Rezk (University of Illinois at Urbana-Champaign)

Date: June 1 - 19, 2015; Mondays and Wednesdays, 10:15 - 12:00

Venue: HIM lecture hall (Poppelsdorfer Allee 45) and MPIM lecture hall (Vivatsgasse 7)

  • HIM lecture hall: June 1; 10:15 - 12:00 (Welcome coffee: 9:45 - 10:15)
  • HIM lecture hall: June 3; 10:15 - 12:00
  • HIM lecture hall: June 8; 10:15 - 12:00
  • HIM lecture hall: June 10; 10:15 - 12:00
  • MPIM lecture hall: June 15; 10:15 - 12:00
  • MPIM lecture hall: June 17; 10:15 - 12:00

Video recording: HCM Youtube Channel



Elliptic cohomology theories have been studied for almost thirty years. Though a great deal has been learned about elliptic cohomology, there are still many mysteries. Their fascination lies in the way they interrelate three different fields: mathematical physics, homotopy theory, and arithmetic algebraic geometry.

The goal of this series of talks is to give a survey of the interplay between two of these three aspects of elliptic cohomology theories: their construction using the modern methods of homotopy theory (which includes what has come to be known as higher category theory), and their interpretation in terms of the arithmetic moduli of elliptic curves. A major theme will be to describe how the problem of putting rigid homotopy theoretic structures on elliptic cohomology (e.g., building it as a highly structured commutative ring spectra) necessarily forces a close study of the theory of isogenies of elliptic curves, and of their formal groups. I hope also to highlight many of the mysteries which still remain.