Randy McCarthy's Vita

\ Randy McCarthy's Vita

Randy McCarthy
Email: randy@math.uiuc.edu
324 Illini Hall, (217)-244-7307
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

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

Papers to appear

with Brenda Johnson, Taylor towers of symmetric and exterior powers.pdf, Fundamenta Mathematicae.

with Michele Intermont, Brenda Johnson, The rank filtration and Robinson's complex, J. Pure Appl. Algebra

Preprints

with Ayelet Lindenstrauss, The Algebraic K-theory of Extensions of a Ring by Direct Sums of Itself

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