Prof. Dr. Gregory James Pearlstein

Texas A&M University
Mathematics

External Senior Fellow
Marie S. Curie FCFP Fellow
June – August 2019

E-Mail: gpearl@math.tamu.edu

Last Update: 31.08.2019

Curriculum Vitae

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:

Boundary components of Mumford-Tate domains.

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.

Selected Publications

B oundary c omponents of Mumford-Tate domains, (with M. Kerr), Duke Math. Journal, 165 (2016), 661-721.
On the algebraicity of the zero locus of an admissible normal function (with P. Brosnan), Compositio Math., 149 (2013), 1913-1962.
Singularities of admissible normal functions(with P. Brosnan, H. Fang, Z. Nie), Invent. Math., 177 (2009) 599-629.
The zero locus of an admissible normal function(with P. Brosnan), Annals of Math., 170 (2009), 883-893.
SL ₂ orbits and degenerations of mixed Hodge structure, J. Diff. Geom, 74 (2006), 1-67.

FRIAS Project

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 νdefines 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 νobstructs 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.