"Weyl Law at 100"

University Of California-Berkeley, Berkeley CA

Investigators

Abstract

Abstract (Zworski, 1216660) This award provides funding to help defray the expenses of participants, especially women, graduate students, postdocs, and junior faculty, in the "The Weyl Law at 100" conference that will be held from September 19--22, 2012, at the Fields Institute for Research in Mathematical Sciences in Toronto, Canada. In 1912 Hermann Weyl published his paper establishing the Weyl law which gives the leading asymptotic description for the counting function of eigenvalues of the Dirichlet or Neumann Laplacian on a bounded domain in the Euclidean space. He later conjectured the form of the second term in asymptotics of the counting functions. After contributions by many mathematicians, among them, Courant, Hilbert, Agranovitch, Levitan, Hormander, Seeley, Duistermaat, Guillemin, Melrose and Sjostrand, the Weyl conjecture was solved by Ivrii in 1982. The workshop is intended as a forward-looking celebration of the 100th anniversary of Weyl's paper. Among the directions to be explored are the (conjectured) connection between random matrix theory and high energy distribution of differences between eigenvalues, probabilistic Weyl laws for non-self-adjoint operators, distribution of scattering resonances and fractal Weyl laws, and physical experiments related to quantum chaos and inverse problems. All of the conference topics are central to analysis and are extremely active areas of research. The conference will bring together a broad spectrum of accomplished researchers thereby providing ample opportunities to develop collaborative interactions, and the format of the meeting is such that young people will have ample opportunities to speak and be otherwise engaged in the various conference activities.