Jerome William Hoffman
Last Updated : September 28, 2010
Rank : Professor of Mathematics
Degree : Ph.D.- Harvard University, (advisor Heisuke Hironaka)
A.B.- Princeton University
Office : 374 Lockett Hall
Address: Department of Mathematics, LSU, Baton Rouge, LA 70803-4918
Phone : 225-578-1575
Fax : 225-578-4276
E-mail : email@example.com
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.
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.
5.) Here is the link for Math 4031, Fall 2008.
Interests: Algebraic Geometry. Over the
past few years the main focus has been
1.) Topology and
Siegel modular threefolds. These are quotients of the Siegel upper half
of degree 2 and they
parametrize families of abelian varieties of dimension 2. This has been
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
3.) Pseudozeros of polynomial equations. This is a
Hong Zhang and
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
arise as quotients of the Bruhat-Tits building for GL(2) of a local
Problem: what are the analogs of these for
other algebraic groups, and their connection to moduli spaces (Shimura
Drinfeld moduli spaces)?
5) Axiomatic homotopy theory and connections to
curves and modular forms.
Zeta functions of graphs,
modular forms, and dynamical systems.
3.) Topology of Siegel 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
for noncongruence subgroups.
8.) Infinitesimal structure
of Chow groups.
9.) Zeta functions of buildings
and algebraic geometry.
10.) Algebraic curves of GL(2)-type.
11.) Arithmetic properties of Picard-Fuchs