For the past decade, the Institute’s Science Initiative Group (SIG) has worked with the World Bank and other partners to strengthen science in developing nations. In this talk, Phillip Griffiths, who helped create SIG when he was Director of the Institute from 1991 to 2003, will address the context for and evolution of SIG’s programs, with emphasis on the new Carnegie–IAS Regional Initiative in Science and Education (RISE), which prepares Ph.D.-level scientists and engineers in sub-Saharan Africa through university-based research and training networks.
Although the concept of randomness is ubiquitous, it turns out to be difficult to generate a truly random sequence of events. The need for “pseudorandomness” in various parts of modern science, ranging from numerical simulation to cryptography, has challenged our limited understanding of this issue and our mathematical resources. In this talk, Professor Jean Bourgain explores some of the problems of pseudorandomness and tools to address them.
Simonyi Hall Seminar Room
A five day workshop focusing on the theory of nonlinear PDEs and their applications to problems in geometry. Topics include conformal geometry, mass transportation, and free boundary problems.
This series of three talks will give a nontechnical, high level overview of geometric complexity theory (GCT), which is an approach to the P vs. NP problem via algebraic geometry, representation theory, and the theory of a new class of quantum groups, called nonstandard quantum groups, that arise in this approach. In particular, GCT suggests that the P vs. NP problem in characteristic zero is intimately linked to the Riemann Hypothesis over finite fields. No background in algebraic geometry, representation theory or quantum groups would be
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.
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.
L.C Evans, PDE and Monge-Kantorovich mass transfer. Current developments in Mathematics, 1997. Int. Press, Boston, (1999).