This page contains some references to background on my research topics. See also Publications for a list of my publications and descriptions of some of my current research projects.

## Goodwillie Calculus

The main references for the calculus of homotopy functors are Goodwillie's original sequence of papers:*Calculus I, The first derivative of pseudoisotopy theory*, Tom Goodwillie, K-Theory 4 (1990), no. 1, 1--27.*Calculus II, Analytic functors*, Tom Goodwillie, K-Theory 5 (1991/92), no. 4, 295--332.*Calculus III, Taylor series*, Tom Goodwillie, Geometry and Topology 7 (2003) 645-711.

*The derivatives of homotopy theory*, Brenda Johnson, Trans. Amer. Math. Soc. 347 (1995), no. 4, 1295--1321.*The Goodwillie tower of the identity functor and the unstable periodic homotopy of spheres*, Greg Arone and Mark Mahowald, Invent. Math. 135 (1999), no. 3, 743--788.*Partition complexes, Tits buildings and symmetric products*, Greg Arone and Bill Dwyer, Proc. London Math. Soc. (3) 82 (2001), no. 1, 229--256.*Bar constructions for topological operads and the Goodwillie derivatives of the identity*, Michael Ching, Geom. Topol. 9 (2005), 833--933.

*A chain rule in the calculus of homotopy functors*, John Klein and John Rognes, Geom. Topol. 6 (2002), 853--887.*The curious history of Faà di Bruno's formula*, Warren Johnson, Amer. Math. Monthly 109 (2002), no. 3, 217--234.*A chain rule for Goodwillie derivatives of functors from spectra to spectra*, Michael Ching, Trans. Amer. Math. Soc. 362 (2010), no. 1, 399--426.*Operads and chain rules for the calculus of functors*, Greg Arone and Michael Ching, to appear in*Astérisque*

*Taylor towers for functors of additive categories*, Brenda Johnson and Randy McCarthy, J. Pure Appl. Algebra 137 (1999), no. 3, 253--284.*Dual calculus for functors to spectra*, Randy McCarthy,*Homotopy methods in algebraic topology*(Boulder, CO, 1999), 183--215, Contemp. Math., 271, Amer. Math. Soc., Providence, RI, 2001.*Deriving calculus with cotriples*, Brenda Johnson and Randy McCarthy, Trans. Amer. Math. Soc. 356 (2004), no. 2, 757--803.

## Operads

The theory of Koszul duality for operad has been particularly significant in my work:*Koszul resolutions*, Stewart Priddy, Trans. Amer. Math. Soc. 152 1970 39--60.*Koszul duality for operads*, Victor Ginzburg and Mikhail Kapranov, Duke Math. J. 76 (1994), no. 1, 203--272.*Operads, homotopy algebra, and iterated integrals for double loop spaces*, Ezra Getzler and John Jones, preprint.*Koszul duality of operads and homology of partition posets*, Benoit Fresse,*Homotopy theory: relations with algebraic geometry, group cohomology, and algebraic $K$-theory*, 115--215, Contemp. Math., 346, Amer. Math. Soc., Providence, RI, 2004.

*Operads and moduli spaces of genus $0$ Riemann surfaces*, Ezra Getzler,*The moduli space of curves*(Texel Island, 1994), 199--230, Progr. Math., 129, Birkhäuser Boston, Boston, MA, 1995.*Modular operads*, Ezra Getzler and Mikhail Kapranov, Compositio Math. 110 (1998), no. 1, 65--126.

## Algebraic K-theory of ring spectra

The Taylor tower of the algebraic K-theory functor has been studied in various ways by Randy McCarthy and coauthors:*Stable K-theory and topological Hochschild homology*, Bjørn Ian Dundas and Randy McCarthy, Ann. of Math. (2) 140 (1994), no. 3, 685--701.*The Taylor towers for rational algebraic K-theory and Hochschild homology*, Ruth Kantorovitz and Randy McCarthy, Homology Homotopy Appl. 4 (2002), no. 1, 191--212.*The algebraic K-theory of extensions of a ring by direct sums of itself*, Ayelet Lindenstrauss and Randy McCarthy, Indiana Univ. Math. J. 57 (2008), no. 2, 577--625.

## Michael Ching

Department of Mathematics

Amherst College

PO Box 5000

Amherst, MA 01002

USA

Telephone: (413) 542-5530

Fax: (413) 542-2550

Email: mching@amherst.edu

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