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For more information, contact Philippe Rigollet and Laurent Demanet
Fall 1999
All the talks are at 4:15 pm in Room 2-105. Refreshments are typically served at 3:45 pm in Room 2-349.
Fall 1999 Organizers: Michael Brenner and Daniel Spielman
| Date | Speaker / Abstract |
|---|---|
| Sept. 13 | Maurice van Putten (MIT) |
| Sept. 20 | No Seminar (Yom Kippur) |
| Sept. 27 | Martin Bazant (MIT) Renormalization Groups and Central Limit Theorems in Percolation Percolation is a simple model for spatial disorder, which amounts to randomly coloring each of N sites in a periodic lattice either black or white with probability p and then identifying "clusters" of adjacent black sites. Percolation is a cornerstone of statistical physics because it displays a "phase transition" with critical point pc. The "order parameter" for the phase transition is the size S of the largest cluster as : For p <pc it is typically "small", S=O(log N), while for p>pc it is "large", S=O(N). In this talk, mathematical analysis and computer simulations are presented for the finite-size scaling of the probability distribution FN(S), and connections are revealed between renormalization group methods in physics and the limit theorems of probability theory.(No knowledge of physics is assumed, only basic probability.) |
| Oct. 4 | Juan Maldacena Harvard University QCD, Strings and Black Holes: The Large N limit of field theories and gravity QCD (Quantum Cromodynamics) is believed to be the theory for strong interactions. However, despite its successes to describe high energy processes it has not been possible to do calculationsat low energies (e.g. calculate the mass of the proton). It is believed that a large N (N is the number of colors) approximation would simplify the theory. Furthermore, this simplified theory would be a free string theory.We consider a supersymmetric version of QCD where one can find this string theory quite explicitly. The strings move in a higher dimensional space, and they describe a quantum theoryof gravity in this higher dimensional space. higher dimensional space, and they describe a quantum theory of gravity in this higher dimensional space. This leads, on the one hand, to an explicit solution for the large N dynamics of this theory, and on the other hand, to a description of quantum gravity, quantum black holes, etc., in terms of a conventional field theory. |
| Oct 11 | Columbus Day |
| Oct 18 | Eric Rains AT&T Labs Algebraic aspects of increasing subsequences There has recently been an upsurge of activity related to the distribution of the length of the longest increasing subsequence of a random permutation, caused in large part by the recent discovery by Baik, Deift, and Johansson of an asymptotic connection between increasing subsequences and (complex Hermitian) Gaussian random matrices. Underlying their initial proof was an exact relation between the increasing subsequence problem and certain integrals over the unitary group. In this talk, I will describe this relation, as well as generalizations to multisets, involutions, etc., with particular attention to a new interpretation and proof in terms of invariant theory. In particular, for each of the unitary, orthogonal, and symplectic groups, one can describe the joint invariants of a collection of tensors in terms of increasing subsequences of multisets; in the case of the unitary group, this specializes to the classical straightening algorithm. Time permitting, I will also discuss some asymptotic consequences. |
| Oct 25 | W. R. Peltier The upscale turbulent cascade: shear layers, cyclones and gas giant bands |
| Nov 1 | Martin Nowak Institute for Advanced Study |
| Nov 8 | David Bayer Columbia |
| Nov 15 | Shang-Hua Teng UIUC and Akamai |
| Nov 22 | no seminar |
| Nov 29 | Ashvin Chhabra JP Morgan |
| Dec 6 | Svante Littmarck COMSOL, Inc. FEMLAB - Multiphysics in MATLAB FEMLAB is a general software package for modelling applied physics problems in MATLAB. FEMLAB is built for modelling in many different fields, such as Electromagenetics, Chemical Reactors, Structural Mechanics, and Fluid Dynamics. Specifically, FEMLAB supports the integration of problems from different fields - multiphysics - and integration with dynamical systems through SIMULINK. FEMLAB uses the Finite Element Method for space discretization, and the method of lines for time discretization. FEMLAB has advanced mesh adaption capabilities, and includes a multigrid solver. We present a few applications from the list below:
Academic (benchmark) examples:
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