## Imaging of Small Inhomogeneities, Homogenization and Super Resolution

Yves Capdeboscq

University of Oxford; Institute for Advanced Study

October 8, 2010

Yves Capdeboscq

University of Oxford; Institute for Advanced Study

October 8, 2010

Institute for Advanced Study

September 1, 2010

Jean-Marc Fontaine

University of Paris-Sud 11; Institute for Advanced Study

October 14, 2010

Jeremy Mason

Institute for Advanced Study

October 12, 2010

Pierre Colmez

National Center for Scientific Research

October 7, 2010

(Introduction to the Lecture Series and and overview for those unable to attend the whole Lecture Series)

September 1, 2010

Frank Calegari

Northwestern University; Member, School of Mathematics

October 6, 2010

Frank Calegari

Northwestern University; Member, School of Mathematics

October 13, 2010

Swastik Kopparty

Institute for Advanced Study

September 28, 2010

Van Vu

Rutgers, The State University of New Jersey

September 27, 2010

The condition number of a matrix is at the heart of numerical linear algebra. In the 1940s von-Neumann and Goldstine, motivated by the problem of inverting, posed the following question:

(1) What is the condition number of a random matrix ?

During the years, this question was raised again and again, by various researchers (Smale, Demmel etc). About ten years ago, motivated by "Smoothed Analysis", Spielman and Teng raised a more general question:

(2) What is the condition number of a randomly perturbed matrix ?