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Randy McCarthy's Vita
Randy McCarthy
Email:
rmccrthy@illinois.edu
Mailing address: 608 S Wright St, Suite 112, 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
Associate Chair for Instructional Technology, 2013--present
Director of NetMath, 2013--present
Director of Undergraduate Studies in Mathematics, 2015--2019
Director Graduate Studies in Math at UIUC, 2009-2012
Director Undergraduate Studies in Math at UIUC, 2004--2007
Professor, University of Illinois, 2005--present
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