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

Avi Wigderson
Institute for Advanced Study
October 24, 2008 (All day)

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 (All day)

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.


The Fifth Element: Astronomical Evidence for Black Holes, Dark Matter, and Dark Energy

Scott Tremaine
Institute for Advanced Study
October 15, 2008 (All day)

Scott Tremaine, Richard Black Professor, School of Natural Sciences
One of the remarkable successes of twentieth century astronomy was the demonstration that the laws of physics derived in the laboratory can successfully describe a wide range of astronomical objects and phenomena. One of the great hopes of twenty-first century physics is that astronomy can return the favor, by allowing us to explore physics that cannot be studied in the laboratory. As examples, Professor Tremaine described three exotic forms of matter that (so far) are known to exist only from astronomical observations: black holes, dark matter, and dark energy.


Geometric PDE - Fully Nonlinear Equations in Conformal Geometry

Matthew Gursky
Institute for Advanced Study
October 7, 2008 (All day)

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.

Next, I will discuss a prori estimates, some basics of blow-up analysis, and entire solutions.


Half-Moon Needle in the Silk Rain Forest

Sheila Hicks
Artist and creator of "Green Silk Forest"
October 7, 2008 (All day)

Artist Sheila Hicks created Green Silk Forest, the tapestry bas-relief installed in the Institute Dining Hall last winter. She speaks about projects she has completed in Europe, the Middle East, North Africa, Japan, and the United States, and she discusses the concepts and construction techniques she uses to create her work.


CSDM - Lower Bounds for Circuits with MOD_m Gates

Arkadev Chattopadhyay
Institute for Advanced Study
October 7, 2008 (All day)

Let CC_{o(n)} \left[ m \right] be the class of circuits that have size o(n) and in which all gates are MOD_m gates.