School of Mathematics

The "P vs. NP" Problem: Efficient Computation, Internet Security, and the Limits of Human Knowledge

Avi Wigderson
Institute for Advanced Study
October 24, 2008

The "P vs. NP" problem is a central outstanding problem of computer science and mathematics.  In this talk, Professor Wigderson attempts to describe its technical, scientific, and philosophical content, its status, and the implications of its two possible resolutions.

Geometric PDE - Variational techniques for the prescribed Q-curvature equation

Andrea Malchiodi
Institute for Advanced Study
October 21, 2008

http://www.math.ias.edu/sp/gpde

 

After recalling the definition of Q-curvature and some applications, we will address the question of prescribing it through a conformal deformation of the metric. We will address some compactness issues, treated via blow-up analysis, and then study the problem, which has variational structure, using a Morse-theoretical approach.

Geometric PDE - Fully Nonlinear Equations in Conformal Geometry

Matthew Gursky
Institute for Advanced Study
October 7, 2008

http://www.math.ias.edu/sp/gpde

The goal of this course to provide an introduction to Monge-Ampere-type equations in conformal geometry and their applications.

The plan of the course is the following: After providing some background material in conformal geometry, I will describe the k-Yamabe problem, a fully nonlinear version of the Yamabe problem, and discuss the associated ellipticity condition and its geometric consequences.

Atle Selberg Memorial

January 11, 2008

Atle Selberg

Memorial Program in Honor of His Life & Work
January 11-12, 2008

Renowned Norwegian mathematician Atle Selberg, Professor Emeritus in the School of Mathematics at the Institute for Advanced Study, died in 2007 at the age of 90.  Throughout a career spanning more than six decades, Professor Selberg made significant contributions to modular forms, Riemann and other zeta functions, analytic number theory, sieve methods, discrete groups, and trace formula. A memorial program in honor of his life and work was held in January 2008.

The Mathematical Infinity

Enrico Bombieri
Institute for Advanced Study
January 31, 2007

VaseThis lecture by Enrico Bombieri, IBM von Neumann Professor in the School of Mathematics, explores how mathematics has arrived at its present pragmatic view of infinity and some of the counterintuitive paradoxes, as well as some of the positive results, deriving from its acceptance. It concludes with a view of how computer science is leading today to a new precise concept, namely the impossibly large in the realm of the finite. 

Kurt Gödel Centenary

Institute for Advanced Study
November 17, 2006

Kurt GodelA Program to Mark the Centenary Year of the Birth of Kurt Gödel was held in Wolfensohn Hall at the Institute for Advanced Study on November 17, 2006. The program, which attracted some three-hundred people, consisted of talks aimed at a general audience on the life and work of Kurt Gödel (1906-1978) and his impact on mathematics, philosophy and computer science.