During the 2007-08 academic year, Roman Bezrukavnikov of MIT will lead a special program on algebraic geometry and physics in representation theory.
The activity in Combinatorics and Theoretical Computer Science at the Institute for Advanced Study will resume on Monday, September 29.
It will take place on Mondays, and will include:
The Combinatorics and Complexity Theory Seminar - Mondays 11 am, starting September 29.
A mini-course on Computational Pseudo-Randomness- Mondays 2 pm, starting October 6
Mini Conference December 10-12th
During term I of the year, School faculty member Jean Bourgain and Van Vu of Rutgers University will lead a program on arithmetic combinatorics. The following is preliminary information about the program.
Organizer: Alice Chang (Princeton University)
During the academic year 2000-2001, the School of Mathematics will host a special program on computational complexity theory at the Institute for Advanced Study. Several senior researchers will be in residence at the Institute for the year, and we expect a large number of junior visitors and post-doctorate fellows. Some topics on which special focus is planned are:
During the academic year of 2009-2010, Enrico Bombieri of the School and Peter Sarnak of Princeton University/Institute for Advanced Study will lead a program on analytic number theory.
The program will have an emphasis on analytic aspects, and particular topics that will be covered include the distribution of prime numbers, sieves, L functions, special sequences as well as additive and combinatorial methods, exponential sums, spectral analysis and modular forms.
A1-homotopy theory is the homotopy theory for algebraic varieties and more generally for schemes which is based on the analogy between the affine line and the unit interval. During this year we will concentrate on two topics. One is the extension of the existing theory of triangulated motives from varieties over fields to general schemes. The main remaining problem there can be reformulated in terms of the A1-homotopy theory as the problem of finding a good recognition principle for T-loop spaces.
James Arthur from the University of Toronto will be in residence at the Institute for the academic year 2000-01 and will be giving an advanced course on the trace formula and applications. In addition, Robert Kottwitz, Diana Shelstad, M. -F. Vigneras, G. Henniart and J. -P. Labesse will be in residence for term II.
The main emphasis is recent developments in non-linear PDE's and the related analysis. This includes themes such as dispersive Hamiltonian equations with critical nonlinearity, the structure of singularity formations for NLS and generalized KDV type equations, Strichartz theory with nonsmooth variable coefficients, aspects of Ginzburg-Landau theory. Over the recent years, there have been a number of significant advances on these various topics, often involving a considerable analytical technology.