\ Randy McCarthy's Vita
Randy McCarthy
Email: rmccrthy@illinois.edu
324 Illini Hall
Mailing address: 1409 W. Green St., Urbana, IL 61801, USA

Mathematics Education

  • Cornell University, Ph. D., June 1990, Cyclic homology of an exact category, advisor Dan Grayson.
  • Michigan State University, B.A., June 1984.
  • Mathematics positions

  • Faculty Director of ATLAS, 2015--present
  • Director of Undergraduate Studies in Mathematics, 2015--present
  • Associate Chair for Instructional Technology, 2013--present
  • Director of NetMath, 2013--present
  • Director Graduate Studies in Math at UIUC, 2009-2012
  • Professor, University of Illinois, 2005--present
  • Director Undergraduate Studies in Math at UIUC, 2004--2007
  • Associate Professor, University of Illinois, 1997--2005
  • Assistant Professor, University of Illinois, 1994--1997
  • Tamarkin Assistant Professor, Brown University, 1990--1994
  • Homboldt Assistant Professor, Bielefeld University, 1991--1992
  • Honors

  • Beckman Associate in the Center for Advanced Study, University of Illinois, 1998--1999.
  • Sloan Research Fellowship, 1996--1998.
  • Sloan Dissertation Fellowship, 1989--1990.
  • Published Papers

  • Morita equivalence and cyclic homology, C.R. Acad. Sci. Paris Ser. I Math., volume 307, 1988, no. 6, pages 211-215, reviewed in MR 89 18028.
  • On fundamental theorems of algebraic $K$-theory, Topology, volume 32 (1993), no. 2, pages 325-328, reviewed in MR 94 19002.
  • On operations for Hochschild homology, Comm. Algebra, volume 21, 1993, no. 8, pages 2947-2965, reviewed in MR 95 19005.
  • The cyclic homology of an exact category, J. Pure Appl. Algebra, volume 93, 1994, no. 3, pages 251-296, reviewed in MR 95 19002.
  • with Bjorn Dundas, Stable $K$-theory and topological Hochschild homology, Ann. of Math. (2), volume 140, 1994, no. 3, pages 685-701, reviewed in MR 96 19005.
  • with Bjorn Dundas, Erratum: "Stable $K$-theory and topological Hochschild homology, Ann. of Math. (2), volume 142, 1995, no. 2, pages 425-426, reviewed in MR 96 19005.
  • with Bjorn Dundas, Topological Hochschild homology of ring functors and exact categories, J. Pure Appl. Algebra, volume 109, 1996, no. 2, pages 425-426, reviewed in MR 97 19001.
  • with Brenda Johnson, Linearization, Dold-Puppe stabilization, and Mac Lane's $Q$-construction, Trans. Amer. Math. Soc., volume 350, 1998, no. 4, pages 1555-1593, reviewed in MR 98 18007.
  • A chain complex for the spectrum homology of the algebraic $K$-theory of an exact category, Algebraic $K$-theory (Toronto, ON, 1996), pages 199-220, Fields Inst. Comm. 16, American Math. Soc., Providence, RI, reviewed in MR 98 19004.
  • Relative algebraic $K$--theory and topological cyclic homology, Acta Math., volume 179, (1997), no. 2, pages 197-222, reviewed in MR 99 19006.
  • with Brenda Johnson, Taylor towers for functors of additive categories, J. Pure Appl. Algebra, volume 137, 1999, pages 253-284, reviewed in MR 2000b:18018 .
  • with Maria Basterra , $\Gamma$-homology, topological Andri-Quillen homology and stabilization , Topology Appl. 121 (2002), no. 3, 551--566, reviewed in MR 922 730.
  • Dual calculus for functors to spectra, Homotopy methods in algebraic topology (Boulder, CO, 1999), 183--215, Contemp. Math., 271, Amer. Math. Soc., Providence, RI, 2001, reviewed in MR 2002c:18009 .
  • On the computation of stabilized tensor functors and the relative algebraic $K$-theory of dual numbers, Trans. Amer. Math. Soc. 353 (2001), no. 6, 2371--2390, reviewed in MR 2001m:19004 .
  • with Ruth Kantorovitz The Taylor towers for rational algebraic K-theory and Hochschild homology, Homology, homotopy and Applications, Vol. 4(1) 2002, 191--212.
  • with Brenda Johnson, A classification of degree $n$ functors. I. , Cah. Topol. Giom. Diffir. Catig. 44 (2003), no. 1, 2--38, reviewed in MR1961524 (2004b:18016) .
  • with Brenda Johnson, A classification of degree $n$ functors. II. , Cah. Topol. Giom. Diffir. Catig. 44 (2003), no. 3, 163--216, reviewed in MR2003579 .
  • with Vahagn Minasian, HKR theorem for smooth $S$-algebras, J. Pure Appl. Algebra 185 (2003), no. 1-3, 239--258, reviewed in MR2006429
  • with Brenda Johnson, Deriving calculus with cotriples, Trans. Amer. Math. Soc. 356 (2004), no. 2, 757--803, reviewed in MR2022719
  • with Ayelet Lindenstrauss, The Algebraic K-theory of Extensions of a Ring by Direct Sums of Itself, Indiana Univ. Math. J. 57 (2008), no. 2, 577--625.
  • with Brenda Johnson, Taylor towers of symmetric and exterior powers.pdf, Fund. Math. 201 (2008), no. 3, 197--216.
  • with Michele Intermont, Brenda Johnson, The rank filtration and Robinson's complex, J. Pure Appl. Algebra 212 (2008), no. 4, 735--752.
  • with Ayelet Lindenstrauss, On the Algebraic K-theory of Formal Power Series, J. K-Theory 10 (2012), no. 1, 165--189.
  • with Ayelet Lindenstrauss, On the Taylor Tower of Relative K-theory, Geom. and Topol. 16 (2012), no. 2, 685--750.
  • with Kristine Bauer, Brenda Johnson, Cross efects and calculus in an unbased setting, Trans. Amer. Math. Soc. 367 (2015), no. 9, 6671--6718.
  • Published Books

  • with Bjorn Dundas, with Thomas Goodwillie, \ \ \ The local structure of algebraic K-theory, Springer Lec. Note, 2013, xvi+435 pp. ISBN 978-1-4471-4392-5; 978-1-4471-4393-2.
  • Papers to appear

    Preprints

  • with Vahagn Minasian, On Triples, Operads and Generalized Homogeneous Functors.pdf.
  • with Kristine Bauer, On vanishing Tate cohomology and decompositions in Goodwillie calculus.dvi, Tate.ps, Tate.pdf
  • On n-excisive functors of module categories
  • Function complexes for diagrams of simplicial sets