Southwest Center
Distinguished Lecture Series

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 video of his lectures:

• Lectures 1 and 2: video
• Lecture 3: video
• Lecture 4: video
• Lecture 5: video

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

Video of his lectures:

• Lecture 1: video
• Lecture 2: video
• Lecture 3: video
• Lecture 4: video
• Lecture 5: video

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).

Video of his lectures:

• Lecture 1: video, slides.
• Lecture 2: video, slides.
• Lecture 3: video, slides.
• Lecture 4: video, slides.

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 G_m 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.