Jerome William Hoffman
Last Updated : August 28, 2007
Rank : Professor of Mathematics
Degree : Ph.D.- Harvard University, 1977 (advisor Heisuke Hironaka)
A.B.- Princeton University, 1973
Office : 374 Lockett Hall
Address: Department of Mathematics, LSU, Baton Rouge, LA 70803-4918
Phone : 225-578-1575
Fax : 225-578-4276
E-mail : hoffman@math.lsu.edu
Teaching
1.) Over the years I have taught a variety of advanced graduate
courses, including: Algebraic Geometry, Commutative Algebra,
Elliptic Curves, Modular Forms, Algebraic Topology, Number Theory,
Lie Groups and Lie Algebras. For the notes of a
course, taken by students on local and global fields, culminating
inTate's thesis, see Spring 2000 : Math 7290
2.) I have also been teaching in the REU (Research Experience for
Undergraduates) program for the past 5 summers. See the LSU
REU link. I
have mentored students in many projects, including: zeta functions and
modular forms for genus 2 curves, classical invariant theory, zeta
functions of graphs. Last summer we explored dessins d'enfants. See Vita
for titles
of projects.
3.) Here are notes taken by students
from an Algebraic Geometry course in Fall 2005. Math7280
4.) Here is the link to the
WebWorks
login page for Math 1553, Spring 2008.
Research
Interests: Algebraic Geometry. Over the
past few years the main focus has been
1.) Topology and
geometry of
Siegel modular threefolds. These are quotients of the Siegel upper half
space
of degree 2 and they
parametrize families of abelian varieties of dimension 2. This has been
a collaborative
project with Steven Weintraub .
2.) Regularity of toric varieties. In collaboration with H. Wang,
we have introduced a generalization of Castelnuovo-
Mumford regualrity for
multiprojective spaces. This has application to algorithms for solving
systems of polynomial equations.
Further generalizations have been
introduced by D. Maclagan and G. Smith and are currently
under investigation.
3.) Pseudozeros of polynomial equations. This is a
collaboration with
Hong Zhang and
James Madden.
This also has to
do with efficient algorithms for
solving polynomial systems.
4.) Zeta functions of graphs and buildings. Yasutaka Ihara
introduced the zeta function of graphs and found links to the zeta
functions of modular curves. These
graphs
arise as quotients of the Bruhat-Tits building for GL(2) of a local
p-adic field.
Problem: what are the analogs of these for
other algebraic groups, and their connection to moduli spaces (Shimura
varieties,
Drinfeld moduli spaces)?
5) Axiomatic homotopy theory and connections to
K-theory.
Expository Lectures:
1.) Elliptic
curves and modular forms.
2.)
Zeta functions of graphs,
modular forms, and dynamical systems.
3.) Topology of Siegel modular
threefolds.
4.) Modular
forms on noncongruence subgroups and Atkin-Swinnerton-Dyer relations.
5.) Picard groups
of Siegel modular threefolds and theta lifting.
6.) Zeta functions of buildings and
Shimura varieties.
7.) L-functions and l-adic representations
for noncongruence subgroups.