The first two Southwest Center grants (1998-2006) provided funds for a Distinguished Lecture Series. As with the Arizona Winter School courses, we tried to ensure as much interaction between speakers, post-docs, and graduate students as possible. In addition to the lectures themselves, these lecture series featured informal question and answer sessions (2 hours a day in some cases!) where the speaker (and other faculty members) gave more details about technical points, motivations, etc.
Notes and (some) video from past lecture series
Greg Anderson: The product of all the numbers in a box
Anderson gave four lectures in April 2006. Here are some related documents:
- “Interpolation of numbers of Catalan type in a local field of positive characteristic” (pdf)
- “A two-variable refinement of the Stark conjecture in the function field case” (pdf)
- See Anderson's web site for related developments.
Christopher Deninger: Arithmetic geometry and analysis on foliated spaces
Deninger gave five lectures in May 2005. Here are notes:
- “Arithmetic geometry and analysis on foliated spaces” (pdf)
and streaming video of his lectures:
Pierre Cartier: From the combinatorics of particle interactions to special values of (multiple) zeta functions
Cartier gave five lectures in February, 2004. Here are some relevant papers:
- “Fonctions polylogarithmes, nombres polyzêtas et groupes pro-unipotents”, Séminaire Bourbaki 885, Mars 2001 (dvi, ps, pdf)
- Several chapters from an upcoming book with Cecile De Witt. All files are pdf:
Chapter 1, Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 9, Chapter 9 bis, Chapter 14, Chapter 16.
- Mathemagics [pdf], or in postscript at the IHES preprint site
H. P. F. Swinnerton-Dyer: New methods for Diophantine
equations
Sir Peter gave four lectures in December, 2002.
He has provided two sets of notes:
- “Diophantine
Equations: Progress and Problems” (pdf)
- “A new method for certain Diophantine equations” (pdf).
Streaming video with slides of his lectures:
Alexander Goncharov:
Multiple zeta-values, Galois groups, and the geometry of modular
varieties
Goncharov gave 5 lectures in May, 2001 on a
mysterious relationship between the structure of the motivic
fundamental group of
Gm minus the N-th roots of
unity and the geometry of modular varieties for
GL
m(Q). There are three relevant articles on the ArXive:
Multiple zeta-values, Galois groups, and geometry of
modular varieties,
Multiple polylogarithms and mixed Tate motives,
and
The dihedral Lie algebras and Galois symmetries of [a
fundamental group].
Takeshi Tsuji: p-adic Hodge theory and arithmetic
Tsuji gave
a series of 4 lectures at USC and Caltech in February, 2001 on various
topics related to p-adic Hodge theory. He provided 2 sets of notes, on
“Explicit reciprocity law for Lubin-Tate groups” (
dvi,
ps,
pdf) and on “Crystalline
sheaves, syntomic cohomology, and p-adic polylogarithms” (
dvi,
ps,
pdf).
David Rohrlich: Crosscurrents in Galois
theory
Rohrlich gave a series of 4 lectures in
December, 2000 about connections between the inverse Galois problem
and division towers (both the usual and “false” division
towers). Many of these results appear in two papers in the Journal of
Algebra:
False division towers of elliptic curves and
A deformation of the Tate module.
Anand Pillay: Model theory and diophantine geometry
Pillay
gave a very intense and very instructive series of 5 lectures in May
2000. Notes by Robert Lakatos are available in
ps and
pdf formats. These notes
contain a few inaccuracies and should be considered as a preliminary
draft, but they may be useful as an introduction to the
model-theoretic proof of the Mordell-Lang conjecture.
Jim Carlson: An introduction to Hodge theory and its
applications
Carlson gave a series of 5 lectures in April 2000
which was attended by members of many groups in the department. Notes
were written by Romyar Sharifi and are available in
dvi,
ps, and
pdf formats.
Ken Ribet:
Torsion points on modular curves and Galois theory
Ribet gave a
series of 5 lectures in May, 1999. He and Minhyong Kim wrote a very
nice set of notes which are available in
dvi,
ps, and
pdf formats.
