Colloquium, Academic Year 2014-2015
Tea at 3:30 pm in 1425 Stevenson Center
August 21, 2014 | Fall faculty assembly, no colloquium |
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August 28, 2014 | The mathematics of three-dimensional structure determination of molecules by cryo-electron microscopy. Cryo-electron microscopy (EM) is used to acquire noisy 2D projection images of thousands of individual, identical frozen-hydrated macromolecules at random unknown orientations and positions. The goal is to reconstruct the 3D structure of the macromolecule with sufficiently high resolution. We will discuss algorithms for solving the cryo-EM problem and their relation to other branches of mathematics such as tomography, random matrix theory, representation theory, spectral geometry, convex optimization and semidefinite programming. Contact person: Alex Powell |
September 4, 2014 | Welcome event, no colloquium |
September 11, 2014 | Contact person: Mark Sapir |
September 18, 2014 | Contact person: Dietmar Bisch |
October 2, 2014 | Contact person: Marcelo Disconzi |
October 9, 2014 | Contact person: Mark Sapir |
October 16, 2014 | Fall break |
October 23, 2014 | Faculty meeting, no colloquium |
October 30, 2014 | Banded matrices and fast inverses. The inverse of a banded matrix A has a special form which we can find directly from the "Nullity Theorem." Then the inverse of that matrix A^-1 is the original A -- which can be found by a remarkable "local" inverse formula. This formula uses only the banded part of A^-1 and it offers a very fast algorithm to produce A. That fast algorithm has a potentially valuable application. Start now with a banded matrix B (possibly the positive definite beginning of a covariance matrix C -- but covariances outside the band are unknown or too expensive to compute). It is a poor idea to assume that those covariances are zero. Much better to complete B to C by a rule of maximum entropy which for Gaussians means maximum determinant. As statisticians and also linear algebraists discovered, the optimally completed matrix C is the inverse of a banded matrix. Best of all, the matrix actually needed in computations is that banded C^-1 (which is not B !).And C^-1 comes quickly and efficiently from the local inverse formula. A very special subset of banded matrices contains those whose inverses are also banded. These arise in studying orthogonal polynomials and also in wavelet theory -- the wavelet transform and its inverse are both banded ( = FIR filters). We describe a factorization for all banded matrices that have banded inverses. Contact person: Akram Aldroubi |
November 6, 2014 | Contact person: Mark Sapir |
November 13, 2014 | Contact person: Jesse Peterson |
November 20, 2014 | Faculty meeting, no colloquium |
November 27, 2014 | Thanksgiving break |
December 4, 2014 | Contact person: Vaughan Jones |
Colloquium Chair (2014-2015): Jesse Peterson