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).

Human Rights Challenges in the Next Decade

Mary Robinson
Former President of Ireland and founder of Realizing Rights: The Ethical Globalization Initiative
October 27, 2008

Mary RobinsonMary Robinson, former President of Ireland and former United Nations High Commissioner for Human Rights, will address the present and future of international human rights as part of the Institute’s Lectures on Public Policy. On the eve of the sixtieth anniversary of the Universal Declaration of Human Rights, Robinson will discuss the need to take stock of current challenges

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.

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

Scott Tremaine
Institute for Advanced Study
October 15, 2008

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.