Elliptic moduli in algebraic topology

Series: 
School of Mathematics Colloquium
Thursday, April 9, 2015 - 11:00
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
MIT
Organizer: 
Much effort in the past several decades has gone into lifting various algebraic structures into a topological context. I will describe one such lifting: that of the arithmetic theory of elliptic curves. The result is a rich and highly structured family of cohomology theories collectively known as elliptic cohomology. By forming "global sections" one is led to a topological enrichment of the ring of modular forms. Geometric interpretations of these theories are enticing but still conjectural at best.