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D-bundles
and Integrable Hierarchies May 14 - 16, 2007
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RESOURCES: What do water waves have to do
with algebraic geometry? (by Peter Miller) Airport shuttle number: 734-394-1665 (reserve 24h in advance) Organizer
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We will spend a few days learning recent work of Thomas Nevins and
David Ben-Zvi: D-bundles and integrable hyerarchies. This work explores a connection between non-commutative geometry and
classical integrable hierarchies. The geometry of D-bundles on cubic curves
is shown to be naturally related - in two different ways - to the KP (Kadomtsev-Petviashvili,
a generalization of the more familiar KdV) and CM (Calogero-Moser)
hierarchies. This provides a conceptual explanation for the observed
phenomenon that the poles of solutions of the KP hierarchy move according to
CM particle systems. Besides providing an interesting bridge between different areas of
mathematics, this work develops and brings toghether many constructions of
great interest to algebraic geometers (Fourier-Mukai transform, Sato (and
adelic) Grassmannian, Hilbert scheme of points on a non-commutative surface
just to mention a few key-words). A survey is presented in the paper From Solitons to Many-Body Systems. A detailed schedule of the talks will appear on this
webpage as details develop. We intend this workshop as an occasion to bring toghether people from
various areas of algebraic geometry (and mathematics in general). For this
reason, the assumed background will be minimal. In the spirit of a
"learning-seminar", most of the talks will be given by non-experts.
David Ben-Zvi and Thomas Nevins have kindly agreed to help facilitate the
workshop, providing expert guidance and a broader perspective. The first talks will be accessible to graduate
students in algebraic geometry and related fields. In addition to the lectures there will be more informal time for
discussion with the authors of the paper, Q&A's, brainstorming, and
development of possible projects for future study.
SCHEDULE ALL TALKS WILL BE
IN EH 4088 ( 4th FLOOR, MAKE A LEFT OUT OF THE ELEVATOR ) ( BREAKFAST AND MUNCHIES IN THE MATH LOUNGE ON THE 2nd
FLOOR ) Carolyn and Toby Stafford are inviting us to a workshop party on Tuesday evening!
Details and directions will appear on this page.
Some funding may be available for outside participants, through the
department's NSF RTG grant. Contact Renzo Cavalieri
for information. Department of Mathematics
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