School of Mathematics

Pseudorandomness in Mathematics and Computer Science Mini-Workshop

Institute for Advanced Study
December 3, 2008

In math, one often studies random aspects of deterministic systems and structures. In CS, one often tries to efficiently create structures and systems with specific random-like properties. Recent work has shown many connections between these two approaches through the concept of "pseudorandomness".

Lectures by Bourgain, Impagliazzo, Sarnak and Wigderson (schedule below), will explore some of the facets of pseudorandomness, with particular emphasis on research directions and open problems that connect the different viewpoints of this concept in math and CS.

Geometric PDE - Optimal transportation and nonlinear elliptic PDE

Neil Trudinger
Institute for Advanced Study
November 11, 2008

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

 

In these lectures we will describe the relationship between optimal transportation and nonlinear elliptic PDE of Monge-Ampere type, focusing on recent advances in characterizing costs and domains for which the Monge-Kantorovich problem has smooth diffeomorphism solutions.

Background references.

L.C Evans, PDE and Monge-Kantorovich mass transfer. Current developments in Mathematics, 1997. Int. Press, Boston, (1999).

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.