PRESIDENTIAL LECTURE SERIES  
2003
 
presents
 

Christopher Sogge
Professor and Chairman Department of Mathematics
Johns Hopkins University

Professor Sogge received his BA from the University of Chicago in 1982, and his PhD from Princeton University in 1985. He was a Dickson Instructor at Chicago and then a Professor at UCLA. He is a recipient of Presidential Young Investigator award and a Sloan Fellowship. He is also was an invited speaker at the prestigious International Congress of Mathematicians in Zurich in 1994.

LECTURE

"Eigenfunctions of the Laplacian"

Thursday, November 6th
10 am

Florida International University (FIU)
Wertheim Conservatory
11200 SW 8th Street, Miami, FL

(Enter FIU through SW 107th Avenue and SW 16th Street)

Arrive early, doors open at 2:30 p.m.
Seating is on a first-come, first-serve basis.
  In this talk we shall go over qualitative and quantitative properties of eigenfunctions. We are particularly interested in the type of sets that they can concentrate on. The quantum correspondence principle suggests that the underlying geometry should allow or not allow concentration. We measure concentration in terms of the size of the eigenfunctions. Following the physicists, we say that there is scarring if the eigenfunctions can blow-up at the maximum possible rate as the eigenvalue goes to zero. In certain cases we can give necessary conditions on the topology of the manifold for there to be scarring for some Riemannian metric. We shall also point out how these issues arise in physical problems.