
Professor Duong Phong
Tue Feb 19, 2008
4:00 pm
We discuss some recent developments in the problem of Khler metrics of constant scalar curvature and stability in geometric invariant theory. In particular, we discuss various notions of stability, both finite and infinitedimensional, and various analytic methods for the problem. These include estimates for energy functionals, density of states...

Institute Professor Isadore Singer
Fri Jan 18, 2008
4:00 pm
The index theorem for an elliptic operator gives an integrality theorem; a characteristic integral over the manifold is an integer because it is the index of the operator. I will review some geometric examples: the Dirac operator on a spin manifold, the spin_C Dirac operator, and their analogues for complex manifolds.
When the manifold has no...

Institute Professor Isadore Singer
Thu Jan 17, 2008
3:30 pm
I'll begin with the Battelle Rencontre "Lectures in Mathematics and Physics" (Seattle, 1967) and end with Sduality as reflected in Mirror Symmetry and in the ElectricMagnetic Duality connection with the Geometric Langlands Program. In between will be a guided tour of special moments in the interaction of mathematicians and high energy theorists...

Robert Grimmett Professor George Papanicolaou
Thu Nov 15, 2007
11:00 am
Broadband, coherent array imaging can be made quite robust in random media by using interferometric
algorithms that tend to minimize the effect of random inhomogeneities. I will introduce and describe these algorithms in detail, and I will
show the results of several numerical simulations that assess their effectiveness.

Robert Grimmett Professor George Papanicolaou
Tue Nov 13, 2007
11:00 am
I will introduce the emerging interdisciplinary field of array imaging with several examples such as sonar, seismic imaging, radar, ultrasonic nondestructive testing, etc. I will explain how resolution issues can be addressed in a unified
mathematical way, along with some new ideas about optimizing the image formation process. I will also show...

Professor Kenneth Ribet
Thu May 24, 2007
4:00 pm
Over the last 15 years, there have been tremendous advances in our understanding of the connections among modular forms, Galois representations and algebraic varieties. Undoubtedly, the most spectacular development in this subject was the proof of Fermat's Last Theorem, which was completed in 1994. Beginning in the late 1960s, JP. Serre...

John Coates
Thu May 10, 2007
4:00 pm
Iwasawa theory, and especially its main conjectures, is the main tool for
studying the mysterious exact formulae in number theory linking the very
different mathematical worlds of purely arithmetic questions on the one
hand, with special values of complex Lfunctions on the other (typified by
the conjecture of Birch and SwinnertonDyer). My...