Applications of monoidal model categories of spectra

Brooke Shipley

I will give an overview of the development of symmetric spectra, orthogonal spectra, and other monoidal model categories of spectra as well as some generalizations and applications. I then expect small groups to each focus on one of the various references listed below. Reading List: Foundations: M. Hovey, B. Shipley, J. Smith, Symmetric spectra, J. Amer. Math. Soc., 13 (2000), 149–208. (Only the first three sections are essential.) 
 M. Mandell, J. P. May, S. Schwede, B. Shipley, Model categories of diagram spectra, Proc. London Math. Soc. 82 (2001), 441–512. 
Generalizations and applications: 
 M. Hovey, Spectra and symmetric spectra in general model categories, Journal of Pure and Applied Algebra 165 (2001) 63–127. 
 T. Geisser and L. Hesselholt, Topological cyclic homology of schemes. Algebraic K-Theory (Seattle, WA, 1997), 41–87, Proc. Sympos. Pure Math., 67, Amer. Math. Soc., Providence, RI, 1999. (In particular, section 6.1) Available at: http://www-math.mit.edu/∼larsh/papers/008/gh.pdf • B. Shipley, HZ-algebra spectra are differential graded algebras, Amer. J. Math. 129 (2007) 351-379. General reference: • S. Schwede, Symmetric spectra, untitled book in progress. Available at: www.math.uni- bonn.de/people/schwede/SymSpec

https://www.msri.org/workshops/797/schedules/22698

MSRI- Women in Topology