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SUMMARY:Elliptic cohomology and dualizability\, I [MPIM]
DTSTART:20250527T143000Z
DTEND:20250527T160000Z
DTSTAMP:20260416T083200Z
UID:indico-event-453@math-events.uni-bonn.de
DESCRIPTION:Speakers: David Gepner (HJU/MPIM)\n\nIMPRS mini course "Ellipt
 ic cohomology and dualizability"\nThe ring of topological modular forms ar
 ises as functions on the moduli stack of elliptic curves\, suitably interp
 reted in a homotopical sense. To see more of the geometry of elliptic coho
 mology\, we would like to interpret the cohomology of classifying spaces s
 imilarly\, in terms of schemes related to symmetric powers of elliptic cur
 ves.\nIn this minicourse\, we will begin by recalling the link between ell
 iptic curves and chromatic homotopy theory via formal groups\, as well as 
 the related but simpler case of K-theory and the multiplicative group. Nex
 t\, we will describe how an orientation of the formal group allows one to 
 extend elliptic cohomology from topological spaces to topological stacks\,
  and describe the computation of the elliptic cohomology of circle-bundles
 . Finally\, we will consider more general groups\, and indicate why ellipt
 ic cohomology see the of the stack of principal G-bundles as dualizable\, 
 in contrast to the case of K-theory.\nThe prerequisites for this course ar
 e a basic understanding of algebraic topology\, algebraic geometry\, and c
 ategory theory. We will not assume familiarly with spectral algebraic geom
 etry\, though we will introduce this language in an informal way.\n \n\nh
 ttps://math-events.uni-bonn.de/event/453/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/453/
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