BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:A tutorial on constructions of finite complexes with specified coh
 omology (after Steve Mitchell and Jeff Smith) - Nicholas Kuhn (University 
 of Virginia)
DTSTART:20180807T143000Z
DTEND:20180807T153000Z
UID:TALK108646@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Central to the study of modern homotopy theory is the Periodic
 ity Theorem of Mike Hopkins and Jeff Smith\, which says that any type n fi
 nite complex admits a v_n self map.  Their theorem follows from the Devani
 tz-Hopkins-Smith Nilpotence Theorem once one has constructed at least one 
 example of v_n self map of a type n complex.    The construction of such a
 n ur-example uses a construction due to Jeff Smith making use of the modul
 ar representation theory of the symmetric groups.  This followed the first
  construction of a type n complex for all n by Steve Mitchell\, which used
  the modular representation theory of the general linear groups over Z/p. 
  The fine points of the Smith construction are not in the only published s
 ource: Ravenel&#39\;s write-up in his book on the Nilpotence Theorems.  I&
 #39\;ll discuss some of this\, and illustrate the ideas with a constructio
 n of a spectrum whose mod 2 cohomology is free on one generator as a modul
 e over A(3)\, the 1024 dimensional subalgebra of the Steenrod algebra gene
 rated by Sq^1\, Sq^2\, Sq^4\, and Sq^8.  
LOCATION:Seminar Room 2\, Newton Institute
END:VEVENT
END:VCALENDAR