Mathematical Publications: Mark Goresky

1976

  • Geometric cohomology and homology of stratified objects
    (Ph.D. thesis)
    Comments Geometric cycles for cohomology eventually became "perversity 0".

    1977

  • La dualité de Poincaré pour les espaces singuliers (with R.MacPherson),
    C.R. Acad. Sci. Paris, Sér. A 284 (1977), 1549-1551
    Comments Our announcement introducing intersection homology

    1978

  • Triangulation of stratified objects
    Proc. Amer. Math. Soc. 72 (1978), 193-200,

    1980

  • Intersection homology theory (with R. MacPherson)
    Topology 19 (1980), 135-162.

  • L2 cohomology and intersection homology of singular algebraic varieties (with J. Cheeger and R. MacPherson)
    Differential Geometry Princeton University Annals of Math studies, S.T. Yau ed. Sept. 1981.
    Also translated into Russian and published by MIR Press, Moscow USSR.

    1981

  • Whitney stratified chains and cochains
    Trans. Amer. Math. Soc. 267 (1981), 175-196.
    Comments Published version of my thesis

  • On the topology of complex algebraic maps (with R. MacPherson)
    Proc. of Conf. on Algebraic Geometry in La Rabida, Spain.
    Springer Lecture Notes in Mathematics vol. 961 Springer Verlag, N.Y.

    1982

  • Stratified Morse theory (with R. MacPherson)
    Proc. of Symp. in Pure Math. 40 (1983), 517-533
    Comments Announces and illustrates the results on stratified Morse theory


  • Linking pairings on singular spaces (with P. Siegel)
    Comment. Math. Helv. 59 (1983), 96-110.

  • Morse theory and intersection homology (with R.MacPherson)
    Analyse et Topologie sur les Espaces Singulieres,
    Astérisque 101 (1983), 135-192, Société Mathématique de France.

    1983

  • A decomposition theorem for the integral homology of a variety (with J.Carrell)
    Inv. Math. 73 (1983), 367-381.

  • Intersection homology II (with R. MacPherson),\
    Inv. Math. 71 (1983), 77-129
    Comments In 1976 MacPherson explained intersection homology to Pierre Deligne who then offered a conjecture that a derived pushforward and truncation procedure might give the same thing. It was difficult to learn about the derived category at the time. The original manuscript of IH II was widely circulated in 1979, 1980. Many people offered suggestions and the revision was submitted in Oct. 1981 but was lost in the mail. After 8 months we inquired and found that Inventiones had never received the manuscript so it was resubmitted in June 1982 and it appeared in February 1983.


  • Kazhdan-Lusztig polynomials for classical groups.
    (computer tables) Northeastern University preprint.

    1984

  • Four contributions to Seminar on Intersection Homology (A. Borel, ed.):
    1. Witt space cobordism
    2. Lefschetz fixed point theorem (with R. MacPherson)
    3. Sample computation of intersection homology (with R. MacPherson)
    4. Open problems and bibliography for intersection homology (with R. MacPherson)

    Progress in Mathematics vol 50, Birkhauser Boston, 1984.

  • Intersection homology operations
    Comment. Math. Helv. 59 (1984), 485-505.

    1985

  • Lefschetz fixed point formula for intersection homology (with R. MacPherson)
    Comment. Math. Helv. 60 (1985), 366-391.

    1986

  • Simplicial intersection homology (with R. MacPherson)
    Appendix to ``Elementary construction of Perverse Sheaves'' by R. MacPherson and K.Vilonen.
    Inv. Math. 84 (1986), 432-433
    Comments The referee made us take this out of the original paper on intersection homology but many people asked about this so we published it here.

  • Combinatorial geometries, Schubert varieties, and convex polyhedra
    (with I. M. Gelfand, R. MacPherson, and V. Serganova)
    Adv. Math. 63 (1987), 301-316.

    1987

  • On the topology of algebraic torus actions (with R. MacPherson)
    Algebraic Groups: Utrecht 1986, Springer Lecture Notes in Mathematics vol 1271 (1987), 73-90.

    1988

  • Geometry of quadrics and their degenerations (with C. DeConcini, R. MacPherson, and C. Procesi)
    Comment. Math. Helv. 63 (1988), 337-413.

    1989

  • Stratified Morse Theory (with R. MacPherson). Springer Verlag, N. Y. (1989), Ergebnisse vol. 14.  

    (3 MB)  Also translated into Russian and published by MIR Press, Moscow, 1991.

  • Wu numbers of singular spaces (with W. Pardon)
    Topology 28 (1989), 325-367.

    1991

  • Piecewise linear differential forms with poles (with J. P. Brasselet and R. MacPherson)
    American Journal of Mathematics 113 (1991), 1019-1052.

    1992

  • On the Kunneth formula for intersection cohomology (with Daniel Cohen and Lizhen Ji)
    Trans. Amer. Math. Soc. 333 (1992), 63-69.

  • L2 cohomology is intersection cohomology
    The Zeta Function of Picard Modular Surfaces,
    R. Langlands and D. Ramakrishnan, ed., Centre de Recherches Mathematiques, Univ. of Montreal Press, 1992, 47-64.

  • Lefschetz numbers of Hecke correspondences (with R. MacPherson),
    The Zeta Function of Picard Modular Surfaces, R. Langlands and D. Ramakrishnan, ed.
    C.R.M., Univ. of Montreal Press, 1992, 465-478.

    1993

  • The Local contribution to the Lefschetz Fixed Point Formula (with R. MacPherson)
    Inv. Math. 111 (1993), 1-33.

    1994

  • Weighted cohomology (with R. MacPherson and G. Harder)
    Inv. Math. 116 (1994), 139-213.

    1997

  • Discrete series characters and the Lefschetz formula for Hecke operators (with R. Kottwitz and R. MacPherson)
    Duke Math Journal 89 (1997), 477-554

    1998

  • Equivariant cohomology, Koszul duality, and the localization theorem (with R. Kottwitz and R. MacPherson)
    Inv. Math. 131 (1998), 25-83.

  • Toroidal and reductive Borel-Serre compactifications of locally symmetric spaces (with Y.-S. Tai)
    Amer. J. Math. 121 (1998), pp. 1095-1151.

    2000

  • L'algebre de cohomologie du complement, dans un espace affine (with P. Deligne and R. MacPherson)
    Mich. Math. J. 48 (2000), 121-136.

    2002

  • Chern classes of automorphic vector bundles (with W. Pardon)
    Invent. Math. 147 (2002), 561-612.

  • Local intersection cohomology of the Baily-Borel compactification (with G. Harder, R. MacPherson, and A. Nair)
    Compositio Mathematica 134 (2002), 243-268.

    2003

  • The topological trace formula (with R. MacPherson)
    Crelle's J.560 (2003), 77-150.

  • The moduli space of real abelian varieties with level structure (with Y.S. Tai)
    Comp. Math. 139 (2003), 1-27.

  • Anti holomorphic multiplication and a real algebraic modular variety (with Y.S. Tai)
    J. Diff. Geom. 65 (2003), 513-560.

    2004

  • Homology of affine Springer fibers in the unramified case (with R. Kottwitz and R. MacPherson)
    Duke Math. J. 121 (2004), 509-561.

    2005

  • Regular points in affine Springer fibers (with R. Kottwitz and R. MacPherson)
    Michigan Math J. 53 (2005), 97-107.

  • Compactifications of modular varieties
    Harmonic Analysis, The Trace Formula, and Shimura Varieties,
    Proceedings of the Clay Mathematics Institute 2003 Summer School, Fields Institute, Toronto.
    J. Arthur, D. Ellwood, and R. Kottwitz, ed., Amer. Math. Soc. and Clay Math. Inst., 2005, pp. 551-582.

    2006

  • Purity of equivalued affine Springer fibers (with R. Kottwitz and R. MacPherson)
    Representation Theory, 10 (2006), 130-146.

    2009

  • Codimension of root valuation strata (with R. Kottwitz and R. MacPherson)
    Pure and Applied Mathematics Quarterly 5 (2009), 1253-1310.

  • Loop products and closed geodesics (with N. Hingston)
    Duke Math J. 150 (2009), 117-210.

    2010

  • On the spectrum of the equivariant cohomology ring (with R. MacPherson)
    Canad. J. Math. 62 (2010), 262-283.

    2012

  • Hilbert modular forms with coefficients in intersection homology (with Jayce Getz), Birkhauser, 2012

  • Algebraic Shift Register Sequences (with A. Klapper), Cambridge Univ. Press 2012

          

  • Introduction to the papers of R. Thom and J. Mather
    Bull. Amer. Math. Soc. 49 (2012), 469-474.

    2015

  • Euler flag enumeration of Whitney stratified spaces (with R. Ehrenborg and M. Readdy)
       Advances in Mathematics 268 (2015), 85--128

    2018

  • Commentary on "Numbers of Solutions of Equations in Finite Fields" by André Weil
      Bulletin of the AMS 55(3) (2018), 327--329  

    2019

  • Ordinary points mod p of GL(n,R) locally symmetric spaces (with Y. S. Tai)
    Pacific Journal of Mathematics 303(1) (2019), 165-215.

  • Real structures on Dieudonné modules (with Y. S. Tai)
    Pacific Journal of Mathematics 303(1) (2019), 217-241.

  • Armand Borel, 1923-2003 , National Academy of Sciences,
    online collection of biographical memoirs, 2019.

    2020

  • Pfaffian integrals and invariants of singular varieties (with Paolo Aluffi)
    A Panorma of Singularities, F.J.-C. Jiménez, ed.
        Contemporary Mathematics 742 (2020), 1-12. Amer. Math. Soc., Providence R.I., 2020.

  • Morse theory, stratifications and sheaves
    Handbook of Geometry and Topology of Singularities
    (José Luis Cisneros-Molina, Lê Dung Tráng, José Seade ed.), Springer Verlag, N.Y., 2020, pp. 261-320.

    2023

  • Morse theory for discrete magnetic operators and nodal count distribution for graphs (with L. Alon)
    J. Spectral Theory 13 (4) (2023), 1225-1260.

    2024

  • John Mather   Biographical Notes,
    National Academy of Sciences Biographical Memoirs, 2025

  • Topological aspects of Boolean functions (with A. Björner and R. MacPherson)
    Pure and Applied Mathematics Quarterly 20 (2024), 1029-1063.

    2025

  • Nodal count for random signing of a graph with disjoint cycles (with A. Lior)
    J. Spectral Theory 15 (2025), 1337-1365.

  • Smooth critical points of eigenvalues on the torus of magnetic perturbations of graphs (with L. Alon and G. Berkolaiko),
    Arxiv version