Applications of monoidal model categories of spectra
Women in Topology November 29, 2017  December 01, 2017
Location: SLMath: Eisenbud Auditorium
Symmetric spectra
Orthogonal spectra
symmetric monoidal product
54A20  Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
18D15  Closed categories (closed monoidal and Cartesian closed categories, etc.)
5Shipley
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 KTheory (Seattle, WA, 1997), 41–87, Proc. Sympos. Pure Math., 67, Amer. Math. Soc., Providence, RI, 1999. (In particular, section 6.1) Available at: http://wwwmath.mit.edu/∼larsh/papers/008/gh.pdf
• B. Shipley, HZalgebra spectra are differential graded algebras, Amer. J. Math. 129 (2007) 351379.
General reference:
• S. Schwede, Symmetric spectra, untitled book in progress. Available at: www.math.uni bonn.de/people/schwede/SymSpec
Shipley Notes

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