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Sie sind hier: FRIAS Fellows Fellows 2019/2020 Prof. Dr. Gregory James Pearlstein

Prof. Dr. Gregory James Pearlstein

Texas A&M University
Mathematik
External Senior Fellow
Marie S. Curie FCFP Fellow
Juni - August 2019

CV

  • 1999: Ph.D., University of Massachusetts, Amherst.
  • 1992: B.S., University of Massachusetts, Amherst.

Academic Appointments:

    • 2013—Present: Associate Professor, Texas A&M University.
    • 2006–2013: Assistant Professor, Michigan State University.
    • 2005–2006: Visiting Assistant Professor, Duke University.
    • 2004–2005: Member, Institute for Advanced Study, Princeton.
    • 2001–2004: Visiting Assistant Professor, University of California, Irvine
    • 1999–2001: Visiting Assistant Professor, University of California, Santa Cruz.
    • Short term: Max Planck Institute for Mathematics (2002, 2004, 2016), Institute des Hautes Etudes Scientifique (2012, 2010), Universite Joseph Fourier (2009).

Contributions to Science and Research:

Dr. Pearlstein studies asymptotic Hodge theory and its applications to algebraic cycles and moduli.  Among his best know results are:

    • Generalizations of the nilpotent and SL_2 orbit theorems of W. Schmid from variations of pure Hodge structure to variations of mixed Hodge structure.
    • Work on singularities of normal functions and the Hodge conjecture.
    • Proof of the algebraicity of the zero loci of normal functions, and more generally the locus of Hodge classes in a variation of mixed Hodge structure.
    • Boundary components of Mumford-Tate domains.
 

Publikationen (Auswahl)

 

FRIAS-Projekt

Singular metrics and the Hodge conjecture

By the work of M. Green and P. Griffiths et. al., the Hodge conjecture is equivalent to the existence of certain kinds of singularities for holo- morphic sections ν (admissible normal function) of bundles of complex tori J → S arising from Hodge classes on smooth projective varieties. The normal function ν defines an associated biextension line bundle B → S which carries a canonical hermitian structure.  By the work of P. Brosnan and G. Pearlstein, B always extends to any smooth, normal crossing compactification S¯ of S. However, the existence of singularities of ν obstructs the extension of the metric. The object of this project is to understand the Lelong numbers of the biextension metric and their relationship with singularities of normal function, and to give a differential geometric characterization of admissible normal functions.