References

• M. Basterra and M. Mandell, Homology and cohomology of E_∞ ring spectra, Math. Z. 249, 2005.
• T. Goodwillie, Calculus I, K-Theory 4, 1990.
• T. Goodwillie, Calculus II, K-Theory 5, 1991/92.
• T. Goodwillie, Calculus III, Geom. Topol. 7, 2003.
• N. Kuhn, Goodwillie towers and chromatic homotopy: an overview, Geom. Topol. Monogr., 10, 2007.
• B. Johnson and R. McCarthy, Taylor towers for functors of additive categories , J. Pure Appl. Algebra 137, 1999.
• R. McCarthy, Dual calculus for functors to spectra , Contemp. Math., 271, 2001.
• C. Rezk, A streamlined proof of Goodwillie's n-excisive approxmiation, arXiv:0812.1324.
• M. Weiss, Orthogonal Calculus, Trans. Amer. Math. Soc. 347, 1995.

For now at least, our theme is the calculus of (homotopy) functors. Some topics of interest left to cover are

• The definition of degree n functor for n>1.
• The construction of P_n for n>1.
• Classification of homogeneous functors.
• The notion of analytic functor.
• The splitting of the Taylor tower.
• More examples!
• The derivatives of the identity functor on (based) spaces.
• The unbased calculus.

Notes:

• B. Guillou, Talk 1 (5/27/10). The Taylor tower, Degree 1 functors
  
• R. Eldred, Talk 2 (6/3/10). The degree 1 approximation, degree n functors
  
• B. Guillou, Talk 3 (6/24/10). Construction of degree n approximations
  
• B. Guillou, Talk 4 (7/1/10). Homogeneous functors
  
• D. Lior, Talk 5 (7/15/10). The Cotriple Model
  
• R. Eldred, Talk 6 (7/29/10). Degree n functors and n-excisive functors
  
• R. Eldred, Talk 7 (8/12/10). The Taylor Tower of the Forgetful Functor
  

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