Saturday, December 18, 1999

Fine Hall Room 314

11:00 Coffee, Common Room

11:30 Victor Guillemin, MIT, "The Strong Szego Limit Theorem"

1:30 Sergiu Klainerman, Princeton University, "PDE as a unified subject"

2:30 Chris Sogge, Johns Hopkins University, "Global estimates for the wave equation"

3:30 Alice Chang, Princeton University, "Linking the Zeta functional determinant to problems in PDE"

All are welcome! To help the organizers, please e-mail conf99@math.princeton.edu before December 9, 1999 if you are planning to attend.

Topic: Algebraic geometry over the complex numbers by "reduction modulo p" December 15

Presenter: Karen Smith, University of Michigan

Topic: Finally Fun

Presenter: John Conway, Princeton University

Title: Generalizations of Prufer's coding of trees and the December 16

Laplacian and tree polynomials of graphs

Speaker: Alexander Kelmans, Rutgers University and University of Puerto Rico

Abstract: The TREE VOLUME (or tree polynomial) of a graph is, roughly speaking, the "sum" of the Prufer codes of its

spanning trees, where the Prufer code of a tree T with n vertices is a certain word of n-2 letters in the alphabet V(T). The

FOREST VOLUME of a graph G is the tree volume of the graph obtained from G by adding a new universal vertex.

We show that the forest volume of a graph is a natural generalization of its Laplacian polynomial, and many important

properties of Laplacian polynomials can be generalized to forest volumes. This allows us to find a mechanism for obtaining

infinitely many identities that are generalizations of Abel's and Hurwitz's identities. In particular we give a combinatorial

interpretation and proof of Hurwitz's identity.

Topic: Mathematical problems of superfluids December 16

Presenter: Fabrice Bethuel, University of Paris 6

Location: Rutgers, Hill Center, Room 705, tea is available in the 7th floor lounge 3:30 p.m.

Title: Monopoles and relations between four-manifold invariants December 16

Presenter: Paul Feehan, Ohio State University

Topic: An example of points of double concentration: the sonic boom December 17

Presenter: Thierry Aubin, Paris VI